General Group Research Articles

On the modular isomorphism problem for 2-generated groups with cyclic derived subgroup

We continue the analysis of the modular isomorphism problem for [Formula: see text]-generated [Formula: see text]-groups with cyclic derived subgroup, [Formula: see text], started in [D. García-Lucas, Á. del Río and M. Stanojkowski, On group invariants determined by modular group algebras: Even versus odd characteristic, Algebra Represent. Theory 26 (2022) 2683–2707, doi:10.1007/s10468-022-10182-x]. We show that if [Formula: see text] belongs to this class of groups, then the isomorphism type of the quotients [Formula: see text] and [Formula: see text] are determined by its modular group algebra. In fact, we obtain a more general but technical result, expressed in terms of the classification [O. Broche, D. García-Lucas and Á. del Río, A classification of the finite 2-generator cyclic-by-abelian groups of prime-power order, Int. J. Algebra Comput. 33(4) (2023) 641–686]. We also show that for groups in this class of order at most [Formula: see text], the modular isomorphism problem has positive answer. Finally, we describe some families of groups of order [Formula: see text] whose group algebras over the field with [Formula: see text] elements cannot be distinguished with the techniques available to us.

Exploring the rationale of performing vaginal hysterectomy under local anaesthesia: A single-centre experience

IntroductionVaginal hysterectomy (VH) is usually performed under general (GA) or regional anaesthesia. In recent years, the possibility of performing vaginal hysterectomy under local anaesthesia (LA) has also been explored. Our aim was to compare intraoperative and early postoperative outcomes in women who underwent VH under LA with intravenous sedation or GA. MethodsIn this retrospective study, we collected data of patients who underwent VH at our department from June 2021 to December 2022. For every patient, the following data was obtained: hospitalisation duration, type of anaesthesia (LA or GA), accompanying procedures, the dosage of used local anaesthetic in the LA group, maximal pain score for each day of hospitalisation after the procedure, procedure duration, intraoperative blood loss, and postoperative complication rate. Data was analysed using the SPSS Statistics programme. Statistical significance was set at p < 0.05. ResultsSeventy patients were included in the study. The mean age was significantly higher in the LA group compared to GA group (73.8 ± 8.0 years vs. 67.1 ± 9.3 respectively, p-value = 0.003). LA was associated with statistically lower pain scores in the first two days after the procedure (p = 0.003), and shorter procedure duration (p-value <0.001) as well as hospitalisation duration (p < 0.001). Furthermore, the cumulative dosage of different analgesics used during hospitalisation was higher in the GA group. ConclusionsOur results show that LA is a feasible option for patients undergoing VH. Vaginal surgical procedures under LA could be especially beneficial for older patients with medical comorbidities in whom GA would be particularly hazardous.

252 Chronic Subdural Hematoma Drainage Under Local Versus General Anesthesia: Systematic Review and Meta-analysis

INTRODUCTION: Chronic subdural hematoma (CSDH) is one of the most encountered conditions seen in neurosurgery. Although mainstay treatment of cSDH has been burr hole drainage, no consensus yet exists on optimal anesthetic technique for surgical treatment between general (GA) and local (LA) anesthesia. METHODS: A search was conducted in MEDLINE (1946 to November 11, 2022), Embase (1974 to November 11, 2022), and PubMed (up to November 11, 2022). We followed the Preferred Reporting Items for Systematic Reviews and Meta-analyses (PRISMA) guidelines to systematically screen studies. RESULTS: Our literature search identified 521 studies, out of which 20 were included. There were a total of 1750 patients in the LA group and 699 patients in the GA group. Our meta-analysis found that the LA group had significant shorter operative time (mean difference -29.28 minutes, p &lt;0.0001), length of admission (Mean difference -1.58 days, 95% CI = -2.40 to -0.76 days, p = 0.0002), and postoperative complications rate (odds ratio 0.38, 95% CI = 0.25 to 0.59, p &lt; 0.0001) compared to GA. There was no significant difference between the two groups in revision rate (odds ratio 2.71, 95% CI 0.89 to 8.25, p = 0.08) and mortality rate (odds ratio 1.23, 95% CI 0.63 to 2.43, p = 0.55). CONCLUSIONS: In this meta-analysis, LA shows benefits in shorter operative time, shorter admission length, and fewer postoperative complications. This makes local anesthesia a less invasive alternative to general anesthesia especially in elderly patients.

Chronic Subdural Hematoma Drainage under Local versus General Anesthesia: Systematic Review and Meta-Analysis

BackgroundChronic subdural hematoma (CSDH) is one of the most frequently encountered neurosurgical conditions. Although mainstay treatment of cSDH has been burr hole drainage, no consensus yet exists on optimal anesthetic strategy between general (GA) and local (LA) anesthesia. This systematic review compares post-operative outcomes after CSDH evacuation under LA and GA. MethodsA search was conducted in MEDLINE (1946 to November 2022), Embase (1974 to November 2022), and PubMed (up to November 2022). We followed the Preferred Reporting Items for Systematic Reviews and Meta-analyses (PRISMA) guidelines to systematically screen studies. ResultsOur literature search identified 629 studies, out of which 12 were included. There were a total of 1035 patients in the LA group and 699 patients in the GA group. Our meta-analysis found that the LA group had significant shorter operative time (mean difference -29.28 minutes, p <0.0001), length of admission (Mean difference -1.58 days, 95% CI = -2.40 to -0.76 days, p = 0.0002), and postoperative complications rate (odds ratio 0.38, 95% CI = 0.25 to 0.59, p < 0.0001) compared to GA. There was no significant difference between the two groups in revision rate (odds ratio 0.77, 95% CI 0.39 to 1.51, p = 0.45) and mortality rate (odds ratio 1.23, 95% CI 0.63 to 2.43, p = 0.55). ConclusionsIn this meta-analysis, LA shows benefits in shorter operative time, shorter admission length, and fewer postoperative complications. This makes local anesthesia a less invasive alternative to general anesthesia, especially in elderly patients.

The Analysis of Multiple Outcomes between General and Regional Anesthesia in Hip Fracture Surgery: A Systematic Review and Meta-Analysis of Randomized Controlled Trials.

Surgical interventions in hip fracture have been associated with multiple adverse events, including perioperative hypotension and mortality, making the choice of the anesthetic method for this procedure crucial. There is still no consensus on whether regional (RA) or general (GA) anesthesia should be used to maintain hemodynamic stability and more favorable outcomes. Therefore, this meta-analysis examines the differences between RA and GA groups in the incidence of mortality, intraoperative hypotension, and other intra- and postoperative complications. The comparison is essential given the rising global prevalence of hip fractures and the need to optimize anesthesia strategies for improved patient outcomes, particularly in an aging population. We followed PRISMA guidelines (PROSPERO #CRD42022320413). We conducted the search for studies published in English before March 2022 in PubMed, Google Scholar, and the Cochrane Library. We included RCTs that compared general and regional anesthesia in adult patients having hip fracture surgical interventions. The primary outcome was perioperative mortality. The secondary outcomes were peri- or postoperative complications and duration of hospital stay. We conducted a meta-analysis in RevMan (version 5.4). We examined the quality of the methodology with the Cochrane risk of bias 2 tool, while the quality of evidence was determined with GRADE. Fifteen studies with 4110 patients were included. Our findings revealed no significant difference between general and regional anesthesia in risk of perioperative mortality (RR = 1.42 [0.96, 2.10], p-value = 0.08), intraoperative complications, or duration of hospital length of stay. Our results suggest that regional anesthesia and general anesthesia have comparable safety and can be used as alternatives based on specific patient requirements.

Comparison of Oral Health-Related Quality of Life scores in children treated for early childhood caries under general and local anesthesia: a quasi-experimental study.

The purpose of this study was to compare the changes in oral health-related quality of life (OHRQoL) scores in children treated for Early Childhood Caries (ECC) under general (GA) and local anesthesia (LA). A quasi-experimental study was carried out on 73 children, with 37 in the GA group and 36 in the LA group. The early childhood oral health impact scale (ECOHIS) was used to measure OHRQoL, with the type of anesthesia (LA or GA) serving as the explanatory variable. A Friedman test was used to assess the difference between the LA and GA groups at baseline, one-week, and one-month follow-up points. The results showed a significant difference in the overall mean ECOHIS scores between the LA and GA groups at 1-week (LAmean ± SD = 6.12 ± 1.11, GAmean ± SD = 5.50 ± 0.88; P = 0.01) and 1-month (LAmean ± SD = 5.87 ± 1.12, GAmean ± SD = 4.96 ± 0.99; P < 0.001) follow-up points. Irrespective of the administered anesthesia, a significant (P < 0.001) reduction in the mean score for dental pain was observed at both 1-week (mean ± SD = 1.30 ± 1.16) and 1-month (mean ± SD = 0.81 ± 0.89) timepoints after the treatment, as compared to the baseline assessment (mean ± SD = 2.02 ± 1.02). Early treatment for ECC reduces pain, restore normal activities, and improves the quality of life of affected children. Specifically, GA was found to be more beneficial for both children and parents. However, further studies using more robust study designs and carefully considering related factors are necessary to confirm these findings.

The Higman operations and embeddings of recursive groups

Abstract In the context of Higman embeddings of recursive groups into finitely presented groups, we suggest an approach, termed the 𝐻-machine, which for certain wide classes of groups allows constructive Higman embeddings of recursive groups into finitely presented groups. The approach is based on Higman operations, and it explicitly constructs some specific recursively enumerable sets of integer sequences arising during the embeddings. Specific auxiliary operations are introduced to make the work with Higman operations a simpler and more intuitive procedure. Also, an automated mechanism of constructive embeddings of countable groups into 2-generator groups preserving certain “patterns” is mentioned.

Spinal Versus General Anesthesia for Lumbar Decompression or Sequestrectomy in Patients Over 75 Years.

Decompression or sequestrectomy in the lumbar spine can be performed under general (GA) or regional anesthesia. In elderly patients, it is still not clear, which procedure should be chosen. To demonstrate that spinal anesthesia (SA) is a safe choice for lumbar decompression or sequestrectomy in elderly patients. Retrospective clinical single-center study. We included 154 patients with ages over 75 years after lumbar decompression or sequestrectomy. The mean age of the patients was 81 years. Perioperative data (blood loss, dural tear, operative and perioperative time, delirium, urinary retention, and hospital stay) and the postoperative 1-year follow-up (visual analog scale and complication rate). Data were retrospectively collected from patients that underwent lumbar decompression or sequestrectomy between January 2019 and December 2020. The data from the GA and SA groups were compared. SA was performed in 56 patients whereas 98 patients received a GA. There was no clinically relevant difference between both groups with comparable complication rates. The time of surgery, blood loss, perioperative time, and hospital stay time were significantly less in the SA group. SA and GA are both safe and reliable procedures for lumbar decompression or sequestrectomy in elderly patients with no clinically relevant difference.

Free polynilpotent groups and the Magnus property

Abstract Motivated by a classic result for free groups, one says that a group G has the Magnus property if the following holds: Whenever two elements generate the same normal subgroup of G, they are conjugate or inverse-conjugate in G. It is a natural problem to find out which relatively free groups display the Magnus property. We prove that a free polynilpotent group of any given class row has the Magnus property if and only if it is nilpotent of class at most 2. For this purpose we explore the Magnus property more generally in soluble groups, and we produce new techniques, both for establishing and for disproving the property. We also prove that a free center-by-(polynilpotent of given class row) group has the Magnus property if and only if it is nilpotent of class at most 2. On the way, we display 2-generated nilpotent groups (with non-trivial torsion) of any prescribed nilpotency class with the Magnus property. Similar examples of finitely generated, torsion-free nilpotent groups are hard to come by, but we construct a 4-generated, torsion-free, class-3 nilpotent group of Hirsch length 9 with the Magnus property. Furthermore, using a weak variant of the Magnus property and an ultraproduct construction, we establish the existence of metabelian, torsion-free, nilpotent groups of any prescribed nilpotency class with the Magnus property.

Strongly generating elements in finite and profinite groups

Given a finite group G and an element g∈G, we may compare the expected number e(G) of elements needed to generate G and the expected number e(G,g) of elements of G needed to generate G together with g. We address the following question: how large can the difference e(G)−e(G,g) be? We prove that in general this difference can be arbitrarily large. For example for every positive integer n there exists a finite 2-generated group G such that e(G)≥n but e(G,g)≤5 for some g∈G. However, if the derived subgroup of G is nilpotent, then e(G)−e(G,g)≤11 for every g∈G.

Uncountably many permutation stable groups

In a 1937 paper B. H. Neumann constructed an uncountable family of 2-generated groups. We prove that all of his groups are permutation stable by analyzing the structure of their invariant random subgroups.

Is the direct square of every 2-generator simple group 2-generator?

Is the direct square of every 2-generator simple group 2-generator?

Quantifying local embeddings into finite groups

We study a function LΓ which quantifies the LEF (local embeddability into finite groups) property for a finitely generated group Γ. We compute this LEF growth function in some examples, including certain wreath products. We compare LEF growth with the analogous quantitative version of residual finiteness, and exhibit a family of finitely generated residually finite groups which nevertheless admit many more local embeddings into finite groups than they do finite quotients. Along the way, we give a new proof that B.H. Neumann's continuous family of 2-generated groups contains no finitely presented group, a result originally due to Baumslag and Miller. We compare LΓ with quantitative versions of soficity and other metric approximation properties of groups. Finally, we show that there exists a “universal” function which is an upper bound on the LEF growth of any group on a given number of generators, and that (for non-cyclic groups) any such function is non-computable.

On the connectivity of the non-generating graph

Given a 2-generated finite group G, the non-generating graph of G has as vertices the elements of G and two vertices are adjacent if and only if they are distinct and do not generate G. We consider the graph Sigma (G) obtained from the non-generating graph of G by deleting the universal vertices. We prove that if the derived subgroup of G is not nilpotent, then this graph is connected, with diameter at most 5. Moreover, we give a complete classification of the finite groups G such that Sigma (G) is disconnected.

A pro-2 group with full normal Hausdorff spectra

Abstract We construct a 2-generated pro-2 group with full normal Hausdorff spectrum [ 0 , 1 ] [0,1] , with respect to each of the four standard filtration series: the 2-power series, the lower 2-series, the Frattini series, and the dimension subgroup series. This answers a question of Klopsch and the second author, for the even prime case; the odd prime case was settled by the first author and Klopsch. Also, our construction gives the first example of a finitely generated pro-2 group with full Hausdorff spectrum with respect to the lower 2-series.

Potential Influence of Anesthetic Interventions on Breast Cancer Early Recurrence According to Estrogen Receptor Expression: A Sub-Study of a Randomized Trial.

BackgroundEffects of anesthetic interventions on cancer prognosis remain controversial. There is evidence that estrogen receptor (ER)-negative breast cancer patients have an early recurrence peak. We aimed to assess the potential benefit of regional anesthesia-analgesia versus general anesthesia regarding early recurrence in breast cancer according to ER expression.MethodsBased on a multicenter randomized controlled trial (clinicaltrials.gov, NCT00418457), we included all the patients from Peking Union Medical College Hospital research center in this study. The primary outcome was breast cancer recurrence after surgery. The Cox proportional hazard model was used to compare recurrence between groups.ResultsIn total, 1,253 breast cancer patients were included in this sub-study, among whom the median follow-up time was 53 months. In this sub-study, 320 patients were ER-negative, and 933 were ER-positive. As for ER-negative patients, the recurrence risk in the PPA (paravertebral blocks and propofol general anesthesia) group showed no statistical difference compared with the GA (sevoflurane and opioids general anesthesia) group (19.1% versus 23.4%; adjusted HR: 0.80, 95% CI: 0.50–1.30; P = 0.377). In the first 18 months after breast cancer surgery, which is considered as the classical early peak of recurrence, after adjustment for menstruation and the pathological stage of tumor, the decrease of early recurrence observed in the PPA group was not significant compared with the GA group (adjusted HR: 0.63, 95% CI: 0.34–1.14; P = 0.127).ConclusionsIn our study, the effects of early recurrence after breast cancer surgery in both ER-negative and ER-positive patients were similar between regional anesthesia-analgesia and general anesthesia. Large samples of ER-negative patients will be needed to clarify the effects of anesthetic interventions.

On the spread of infinite groups

AbstractA group is $\frac 32$-generated if every non-trivial element is part of a generating pair. In 2019, Donoven and Harper showed that many Thompson groups are $\frac 32$-generated and posed five questions. The first of these is whether there exists a 2-generated group with every proper quotient cyclic that is not $\frac 32$-generated. This is a natural question given the significant work in proving that no finite group has this property, but we show that there is such an infinite group. The groups we consider are a family of finite index subgroups $G_1,\, G_2,\, \ldots$ of the Houghton group $\operatorname {FSym}(\mathbb {Z})\rtimes \mathbb {Z}$. We then show that $G_1$ and $G_2$ are $\frac 32$-generated and investigate the related notion of spread for these groups. We are able to show that they have finite spread at least 2. These are, therefore, the first infinite groups to be shown to have finite positive spread, and the first to be shown to have spread at least 2 (other than $\mathbb {Z}$ and the Tarski monsters, which have infinite spread). As a consequence, for each $k\in \{2,\, 3,\, \ldots \}$, we also have that $G_{2k}$ is index $k$ in $G_2$ but $G_2$ is $\frac 32$-generated whereas $G_{2k}$ is not.

Modern Lower Extremity Bypass Outcomes by Anesthesia Type in the Veteran Population

Lower extremity bypass (LEB) revascularization can be performed under general (GA) or neuraxial anesthesia (NA). Studies show that the use of NA may decrease morbidity, 30-day mortality, and hospital length-of-stay (LOS). The goal of our analysis is to examine the differences in postsurgical outcomes following LEB between patients who undergo GA compared to NA in the Veteran Affairs Surgical Quality Improvement Program (VASQIP) database. After IRB approval, the VASQIP database was assessed for patients who underwent LEB between 1998-2018. Only infrainguinal bypass procedures and anesthesia type classified as "general," "epidural," or "spinal" were included. The neuraxial cohort includes both spinal and epidural anesthesia patients. The Risk Analysis Index (RAI), a validated measure of frailty, was additionally calculated for each patient. Chi squared, paired t-test, and binary logistic regression were used to compare the cohorts. During this period, 22,960 veterans underwent LEB recorded in VASQIP. Compared to those who underwent surgery under GA, patients with procedures performed using NA were older (66.4 ± 9.6 years vs. 65.3 ± 9 years respectively; P <0.001) and more frail (average RAI score 25.7 ± 7.0 vs. 24.9 ± 6.7; P < 0.001). Operative time was shorter in the NA group (4.1 ± 1.7 hrs vs. 4.7 ± 3.0 hrs; P < 0.001) and fewer cases were emergent (1.55% vs. 4.13%; P <0.001). Patients in the GA group had higher rates of postoperative prolonged ileus (0.31% vs. 0.00%; P=0.03), pneumonia (1.60% vs. 1.06%; P=0.025), deep wound infection (2.67% vs. 2.61%; P=0.01), sepsis (1.68% vs. 0.79%; P < 0.001), reintubation (1.80% vs. 1.30%) (P=0.04),and number of packed red blood cell (pRBC) transfused intraoperatively (0.39 ± 1.21 units vs. 0.22 ± 0.79 units; P <0.001). There was no significant difference in rate of graft failure, return to the OR, myocardial infarction, death, or LOS. In regression analysis, those undergoing NA were less likely to require pRBC transfusion intraoperatively (OR: 0.43; 95% CI: 0.31-0.61; P < 0.001), however no other outcomes reached statistical significance. Although younger and less frail, veteran patients undergoing GA for lower extremity revascularization had higher rates of postoperative ileus, pneumonia, deep wound infection, sepsis, and need for transfusion as compared to those undergoing NA. There was no significant difference in the rate of other major complications, myocardial infarction, death or LOS. After adjustment, only intraoperative transfusion remained statistically significant, likely reflecting longer and more complex cases for those that undergo general anesthesia rather than the effect of anesthetic choice itself.

Влияние метода анестезии на объем кровопотери при оперативных вмешательствах на поясничном отделе позвоночника

Актуальность. Операции на поясничном отделе позвоночника могут выполняться в условиях как общей анестезии (ОА), так и спинальной (СА). Одним из преимуществ последней авторы считают уменьшение интраоперационной кровопотери. Однако этот вопрос остается дискуссионным. Цель исследования: сравнить объем кровопотери при операциях на поясничном отделе позвоночника при использовании спинальной и общей внутривенной анестезии. Материалы и методы. В исследование включено 215 пациентов 18–70 лет, ASA I–II, с дегенеративными заболеваниями позвоночника, которым выполнялись плановые оперативные вмешательства с транспедикулярной стабилизацией 1–2 сегментов. Пациентам группы СА (n = 110) выполняли спинальную анестезию 0,5% раствором бупивакаина (4 мл), пациентам группы ОА (n = 105) — общую внутривенную анестезию с искусственной вентиляцией легких (пропофол, фентанил, атракуриум в общепринятых дозах). Жестким условием исследования было поддержание среднего артериального давления (САД) 60–80 мм рт.ст. Результаты. Урапидил для коррекции гемодинамики вводился у 21,9 ± 4,0 % пациентов группы ОА и только у 3,6 ± 1,8 % пациентов группы СА, при этом САД в группе СА был значимо ниже, чем в группе ОА. В результате исследования не выявлено различий в кровопотере (ни по методу Moore, ни по разнице гемоглобина). Однако общее время оперативного вмешательства было статистически значимо больше в группе ОА по сравнению с группой СА (128,5 ± 40,0 мин против 104,6 ± 26,3 мин, р &lt; 0,05). Полученные нами расчеты указывают на сильную корреляционную связь между временем операции и индексом массы тела (r = 0,71, р &lt; 0,05). Выводы. При обеспечении САД 60–80 мм рт.ст. общий уровень кровопотери не зависит от вида анестезии. СА обеспечивает лучший эффект управляемой гипотензии без применения дополнительных фармакологических средств. Время оперативного вмешательства при ОА значимо больше, чем при СА. На него также влияет повышенный индекс массы тела.

Exercise Effects on Neck Function Among F-15E Aircrew

BACKGROUND: Neck pain (NP) is common among high performance aircrew, yet evidence remains insufficient to guide examination, treatment, and prevention. The purpose of this randomized pilot study was to collect baseline data for neck function for F-15E aircrew and determine efficacy and feasibility of two separate exercise protocols in measuring short-term outcomes of subjective and objective neck function in order to inform future study design. METHODS: Randomized to either progressive (PRO) or general (GEN) exercise groups were 41 F-15E aircrew. Data collection occurred at baseline, 3 wk, and 3 mo. RESULTS: At baseline, 39% of the subjects reported current NP, 79.5% reported a history of NP attributed to flying, 12.8% reported being removed from flying duties due to NP, and 10% reported receiving medical care for NP. PRO and GEN group randomization showed similar baseline assessment data. Blinding was successful and exercise logs showed 31.6% compliance with prescribed exercise regimens. There were small but statistically significant increases in neck range of motion in both groups over the course of the study. Aircrew with current NP had significantly higher F-15E flight hours. DISCUSSION: This study supports the high prevalence of NP in aircrew, yet low frequency of seeking care for NP. Future studies to assess NP prevention and treatment in aircrew require an integrated approach that includes operational exercise policy and long-term data collection in flying units with dedicated resources for assessment and analysis. Lee MS, Briggs R, Scheirer V, Kearby G, Young BA. Exercise effects on neck function among F-15E aircrew. Aerosp Med Hum Perform. 2021; 92(10):815824.