Characteristic Subgroup Research Articles

Large characteristic subgroups and abstract group classes

It is well-known that every virtually abelian group contains an abelian characteristic subgroup of finite index. We shall say that a group class is F-characteristic if any group containing an -subgroup of finite index has also a characteristic subgroup of finite index that belongs to . Thus the class of abelian groups is F -characteristic. Many other relevant group classes have recently been proved to be F-characteristic, and the aim of this paper is to give a further contribution to this topic, in particular in the context of classes of generalized nilpotent groups.

Characteristic subgroup lattices and Hopf–Galois structures

The Hopf–Galois structures on normal field extensions [Formula: see text] with [Formula: see text] are in one-to-one correspondence with the set of regular subgroups [Formula: see text] of [Formula: see text], the group of permutations of [Formula: see text] as a set, that are normalized by the left regular representation [Formula: see text]. Each such [Formula: see text] corresponds to a Hopf algebra [Formula: see text] that acts on [Formula: see text]. Such regular subgroups need not be isomorphic to [Formula: see text] but must have the same order. One can divide all such [Formula: see text] into collections [Formula: see text], where [Formula: see text] is the set of those regular [Formula: see text] normalized by [Formula: see text] and isomorphic to a given abstract group [Formula: see text], where [Formula: see text]. There exists an injective correspondence between the characteristic subgroups of a given [Formula: see text] and the set of subgroups of [Formula: see text] stemming from the Galois correspondence between sub-Hopf algebras of [Formula: see text] and intermediate fields [Formula: see text], where [Formula: see text]. We utilize this correspondence to show that for certain pairs [Formula: see text], the collection [Formula: see text] must be empty. This also shows that for these [Formula: see text], there do not exist skew braces with additive group isomorphic to [Formula: see text] and circle group isomorphic to [Formula: see text].

Duality between p-groups with three characteristic subgroups and semisimple anti-commutative algebras

AbstractLet p be an odd prime and let G be a non-abelian finite p-group of exponent p2 with three distinct characteristic subgroups, namely 1, Gp and G. The quotient group G/Gp gives rise to an anti-commutative 𝔽p-algebra L such that the action of Aut (L) is irreducible on L; we call such an algebra IAC. This paper establishes a duality G ↔ L between such groups and such IAC algebras. We prove that IAC algebras are semisimple and we classify the simple IAC algebras of dimension at most 4 over certain fields. We also give other examples of simple IAC algebras, including a family related to the m-th symmetric power of the natural module of SL(2, 𝔽).

Abstract P3-01-18: In vivo isolation of circulating tumour cells using CellCollector and detection of gene mutations in different metastasis organ sites in breast cancer

Abstract Introduction: Metastasis is thought to result from tumour cell entry into the circulation and migration to distant organs, where the mutation landscape of metastatic breast cancer (MBC) may shift and vary. The genotypic features of circulating tumour cells (CTCs) typically differ from those of primary breast cancer (BC) cells. Gene mutation analysis of CTCs in MBC may benefit patients by identifying those amenable to specific therapies. Currently, CTCs are primarily isolated in vitro from small volumes of blood. The aim of this study was to isolate CTCs in vivo using CellCollector and screen for specific gene mutations in cells from different metastasis organ sites and molecular subtypes in MBC patients. Methods: In this study, we used a novel technology, CellCollector, to collect peripheral CTCs. Thirty MBC patients were enrolled, and 17 were analysed with next-generation sequencing (NGS) methods. Clinical characteristics were analysed along with CTC enumeration and detection rates. Whole-genome amplification (WGA) was used to amplify the CTC genomic DNA of 127 genes. Results: We isolated CTCs in vivo from 20 of 30 MBC patients (66.7%), with a median and mean (range) of 2 (0-15) CTCs. In non-cancer patients, no CTCs were detected. We analysed CTC enumeration and the detection rate in different clinical characteristic subgroups. We found that in their corresponding subgroups, patients younger than 45 years old, with brain metastasis, with three or more metastasis organ sites, or with HER2-positive subtypes had the highest CTC medians and means.As far as clinical characteristics were concerned, the number of CTCs seemed correlated with more advanced clinical characteristics. In the one metastasis organ, two metastasis organs and three or more metastasis organs subgroups, the CTC detection rates were 38.5% (5/13), 77.8% (7/9), and 100.0% (8/8), respectively. The CTC detection rate correlated with the number of metastasis organs; patients with more metastasis organ sites had higher CTC detection rates. We also found that different metastasis organs and molecular subtypes contain high-frequency mutation genes, and also contain unique gene mutations. Conclusions: In MBC, CellCollector can be used to collect intact CTCs, from which we can obtain gene mutation information. Different metastasis organs and molecular subtypes may have corresponding unique mutations, which may provide a basis for future gene therapy. CTCs enumeration data and correlations to clinicopathologic characteristicsPatients' characteristics CTCs enumeration RangemedianmeanTotal0-1522Age (years) <450-422≥45 and <600-1512≥600-212Metastatic location Brain0-1556Lung+liver0-712Bone+local recurrence0-411Number of metastatic locations 10-40120-15133-41-723Molecular subtypes Luminal A000Luminal B0-511HER2 positive0-1523Triple negative0-712HER2, human epidermal growth factor receptor 2 Citation Format: Geng C, Li S, Yang S, Shi J, Ding Y, Gao W, Cheng M, Sun Y, Xie Y, Sang M. In vivo isolation of circulating tumour cells using CellCollector and detection of gene mutations in different metastasis organ sites in breast cancer [abstract]. In: Proceedings of the 2018 San Antonio Breast Cancer Symposium; 2018 Dec 4-8; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2019;79(4 Suppl):Abstract nr P3-01-18.

Finite groups with large Noether number are almost cyclic

Noether, Fleischmann and Fogarty proved that if the characteristic of the underlying field does not divide the order |G| of a finite group G, then the polynomial invariants of G are generated by polynomials of degrees at most |G|. Let β(G) denote the largest indispensable degree in such generating sets. Cziszter and Domokos recently described finite groups G with |G|/β(G) at most 2. We prove an asymptotic extension of their result. Namely, |G|/β(G) is bounded for a finite group G if and only if G has a characteristic cyclic subgroup of bounded index. In the course of the proof we obtain the following surprising result. If S is a finite simple group of Lie type or a sporadic group then we have β(S)≤|S| 39/40 . We ask a number of questions motivated by our results.

Impact of patient and disease characteristics on the efficacy and safety of eluxadoline for IBS-D: a subgroup analysis of phase III trials.

Background:Irritable bowel syndrome with diarrhea (IBS-D) is a prevalent gastrointestinal (GI) disorder with a varied presentation, often overlapping with other GI and non-GI disorders. Eluxadoline is a locally active mixed µ- and κ-opioid receptor agonist and δ-opioid receptor antagonist approved for the treatment of IBS-D in adults. As IBS-D is a heterogeneous disease, factors such as patient demographics, symptom severity, and symptom pattern history can potentially inform treatment selection.Methods:Here, we report additional prospectively planned analyses of two large double-blind, placebo-controlled studies (IBS-3001 and IBS-3002) enrolling patients meeting Rome III criteria for IBS-D. Patients were randomized 1:1:1 to receive placebo or eluxadoline 75 mg or 100 mg twice daily. Efficacy (abdominal pain, stool consistency, and composite, simultaneous improvement in both) and safety were assessed for prospectively defined patient subgroups stratified by age, sex, race, presence of comorbidities, and baseline disease characteristics.Results:Across all age, sex, race, comorbidity, and disease characteristic subgroups, a greater proportion of patients were composite responders with both eluxadoline doses as compared with placebo, including patients with a history of depression or a history of gastroesophageal reflux disease. Among patients aged ⩾65 years, a greater proportion of patients receiving eluxadoline 75 mg were composite, abdominal pain, and stool consistency responders compared with those receiving 100 mg. The proportion of patients with at least one adverse event was slightly higher in patients aged ⩾65 years and also in female patients.Conclusions:This analysis suggests that eluxadoline is effective in treating IBS-D across a range of commonly encountered patient types. In contrast to the overall population, patients aged ⩾65 years demonstrated a greater proportion of responders at the lower approved 75 mg eluxadoline dose.

FC-groups with finitely many automorphism orbits

Let G be a group. The orbits of the natural action of Aut(G) on G are called “automorphism orbits” of G, and the number of automorphism orbits of G is denoted by ω(G). In this paper we prove that if G is an FC-group with finitely many automorphism orbits, then the derived subgroup G′ is finite and G admits a decomposition G=Tor(G)×D, where Tor(G) is the torsion subgroup of G and D is a divisible characteristic subgroup of Z(G). We also show that if G is an infinite FC-group with ω(G)⩽8, then either G is soluble or G≅A5×H, where H is an infinite abelian group with ω(H)=2. Moreover, we describe the structure of the infinite non-soluble FC-groups with at most eleven automorphism orbits.

ASS1+hepatocellular adenoma, a new and major subtype

Introduction: A new hepatocellular (HCA) subgroup has been identified among unclassified HCA (UHCA: 10%) using 2 different approaches: gene mutation1 and proteomics2 and 2 immunohistochemical (IHC) methods: PTGDS1 and ASS12 Methods: We reviewed personal and consults resected HCA classified as UHCA, i.e. expressing LFABP, but not CRP, no abnormal GS allowing exclusion of known HCA subtypes. ASS1 was performed by IHC2. Results: We collected 22 personal and 11 consult HCA with ASS1 overexpression in the tumor in comparison with non-tumoral liver. All cases were women and were characteristic on H&E; 5 had borderline lesions, 2 with HCC foci. Clinical data were available in all 22 personal cases: mean age 38 (23-50); 20/20 on oral contraceptives (mean duration 19 years); 15 were overweight (9 with BMI > 30). 7/22 were admitted in emergency for severe hemorrhage and among them 2 had tumors < 5cm. Nodule was solitary in 11 cases; 2 had adenomatosis. Mean size of largest nodule was 7 cm (1.3- 23 cm). 6 patients had arterial hypertension and 5 diabetes. 11/22 cases tested were classified as shHCA1; 2 of them tested by IHC were PTGDS negative. In addition 2 cases classified as UHCA by gene mutation were ASS1+ with H&E characteristics of ASS1+HCA which finally represent 10% in our HCA cohort. Conclusion: ASS1+HCA is a characteristic subgroup both on clinical (hemorrhagic risk even for small tumors) and pathological ground. ASS1 is the 4th marker of the IHC HCA classification. 1Nault et al Gastroenterology 2017; 2Henriet et al Hepatology 2017.

A Note on the Square Subgroups of Decomposable Torsion-Free Abelian Groups of Rank Three

AbstractA hypothesis stated in [16] is confirmed for the case of associative rings. The answers to some questions posed in the mentioned paper are also given. The square subgroup of a completely decomposable torsion-free abelian group is described (in both cases of associative and general rings). It is shown that for any such a group A, the quotient group modulo the square subgroup of A is a nil-group. Some results listed in [16] are generalized and corrected. Moreover, it is proved that for a given abelian group A, the square subgroup of A considered in the class of associative rings, is a characteristic subgroup of A.

Growth changes after inhalant abuse and toluene exposure: A systematic review and meta-analysis of human and animal studies.

Inhalant abuse is a significant public health issue, particularly for adolescents, the predominant group of inhalant users. Adolescence is a critical growth period, and inhalant abuse has been associated with growth impairments, including reduced body weight and height. However, the extent to which inhalant abuse affects growth remains unquantified, and potential moderators remain unknown. To address this knowledge gap, a systematic review and meta-analysis of clinical human and preclinical animal studies utilizing toluene exposure (the primary solvent in abused products) was conducted. Five-hundred and sixty-nine studies were screened; 31 met inclusion criteria, yielding 64 toluene-control comparisons for body weight and 6 comparisons for height. Toluene exposure was negatively associated with body weight ( d = -0.73) and height ( d = -0.69). Concentration of inhaled toluene, but not duration, moderated the effect of toluene exposure on body weight, with more severe impairments at higher concentrations. Differences in effect size for body weight were observed for study characteristic subgroups including sex, age at first exposure, administration route and species. However, these findings should be interpreted cautiously due to low study numbers. Growth impairments, particularly during adolescence, can cause long-term health consequences. These effects on growth are therefore an important clinical outcome for individuals with a history of inhalant abuse.

Large characteristic subgroups with modular subgroup lattice

It is known that if a group contains an abelian subgroup of finite index, then it also has an abelian characteristic subgroup of finite index. The aim of this paper is to prove that corresponding results hold when abelian subgroups are replaced either by subgroups having a modular subgroup lattice or by quasihamiltonian subgroups.

A Note on Large Characteristic Subgroups

ABSTRACTIt is known that if a group G has an abelian subgroup of finite index n, then it contains an abelian characteristic subgroup A of index at most nn. The aim of this paper is to improve this bound by showing that the characteristic subgroup A can be chosen of index at most n2. Examples prove that this bound is the best possible. Our main result is obtained as an application of a general method for the construction of large characteristic subgroups.

Coleman automorphisms of finite groups and their minimal normal subgroups

In this paper, we show that all Coleman automorphisms of a finite group with self-central minimal non-trivial characteristic subgroup are inner; therefore the normalizer property holds for these groups. Using our methods we show that the holomorph and wreath product of finite simple groups, among others, have no non-inner Coleman automorphisms. As a further application of our theorems, we provide partial answers to questions raised by M. Hertweck and W. Kimmerle. Furthermore, we characterize the Coleman automorphisms of extensions of a finite nilpotent group by a cyclic p-group. Finally, we note that class-preserving Coleman automorphisms of p-power order of some nilpotent-by-nilpotent groups are inner, extending a result by J. Hai and J. Ge, where p is a prime number.

Molecular epidemiological characterization of Brucella isolates from sheep and yaks in northwest China.

Animal brucellosis is a re-emerging disease in China with high prevalence in the northwest region. A total of 66 isolates of Brucella were recovered from sheep and yaks in the Inner Mongolia, Xinjiang, Qinghai and Gansu provinces of northwest China in 2015 and 2016. Using classical biotyping and the Brucella AMOS PCR assay, all isolates were identified as Brucella melitensis biovar 3 (n=58), B.melitensis biovar 1 (n=1), Brucella abortus (n=5), or Brucella suis biovar 3 (n=2), and B.melitensis biovar 3 was found to be mainly responsible for sheep brucellosis in northwest China. Multilocus variable-number tandem-repeat analysis (MLVA) was used to identify the epidemiological relationships among the isolates and to assess their genetic diversity. Multilocus variable-number tandem-repeat analysis-16 identified 46 genotypes in these populations, including 37 unique and nine shared genotypes. Multilocus variable-number tandem-repeat analysis-11 showed that 71% of the isolates (47 of 66) were genotype 116 (1-5-3-13-2-2-3-2-4-41-8), a characteristic subgroup of the East Mediterranean group, showing that isolates from different geographical areas exhibit similar epidemiological characteristics in different regions and may be epidemiologically linked. Multilocus variable-number tandem-repeat analysis-11 also revealed that an isolate from Inner Mongolia had a novel genotype, 369 (1-5-3-13-2-2-3-2-7-41-8). Multilocus variable-number tandem-repeat analysis-16 genotyping of northwest China Brucella isolates allows a better understanding of the epidemiology of animal brucellosis in this region. This study is the first analysis of B.melitensis in Gansu province, and the results confirmed that in this province, isolates of this species are disorderly and unsystematic.

Plasma microRNA-based signatures to predict 3-year postoperative recurrence risk for stage II and III gastric cancer.

Our aim was to identify plasma microRNA (miRNA)-based signatures to predict 3-year postoperative recurrence risk for patients with stage II and III gastric cancer (GC), so as to provide insights for individualized adjuvant therapy. Plasma miRNA expression was investigated in three phases, involving 407 patients recruited from three centers. ABI miRNA microarray and TaqMan Low Density Array were adopted in the discovery phase to identify potential miRNAs. Quantitative reverse-transcriptase polymerase chain reaction was used to assess the expression of selected miRNAs. Logistic regression models were constructed in the training set (n = 170) and validated in the validation set (n = 169). Receiver operating characteristic analyses, survival analyses and subgroup analyses were further used to assess the accuracy of the models. We identified a 7 miRNA classifier and 7miR + pathological factors index that provided high predictive accuracy of GC recurrence (area under the curve = 0.725 and 0.841 in the training set; and 0.627 and 0.771 in the validation set). High-risk patients defined by the signatures had significantly shorter disease-free survival and overall survival than low-risk patients. The 7 miRNA classifier is an independent prognostic factor, and could add predictive value to traditional prognostic factors. Subgroup analyses revealed the satisfactory performance persisted regardless of stage, and the two models both displayed high accuracy in stage IIA patients. In conclusion, identified microRNA signature may potentially provide some additional benefit for prediction of disease recurrence in patients with stage II and III GC.

On the structure of virtually nilpotent compact p-adic analytic groups

Abstract Let G be a compact p-adic analytic group. We recall the well-understood finite radical Δ + {\Delta^{+}} and FC-centre Δ, and introduce a p-adic analogue of Roseblade’s subgroup nio ⁢ ( G ) {\mathrm{nio}(G)} , the unique largest orbitally sound open normal subgroup of G. Further, when G is nilpotent-by-finite, we introduce the finite-by-(nilpotent p-valuable) radical 𝐅𝐍 p ⁢ ( G ) {\mathbf{FN}_{p}(G)} , an open characteristic subgroup of G contained in nio ⁢ ( G ) {\mathrm{nio}(G)} . By relating the already well-known theory of isolators with Lazard’s notion of p-saturations, we introduce the isolated lower central (resp. isolated derived) series of a nilpotent (resp. soluble) p-valuable group, and use this to study the conjugation action of nio ⁢ ( G ) {\mathrm{nio}(G)} on 𝐅𝐍 p ⁢ ( G ) {\mathbf{FN}_{p}(G)} . We emerge with a structure theorem for G, 1 ≤ Δ + ≤ Δ ≤ 𝐅𝐍 p ⁢ ( G ) ≤ nio ⁢ ( G ) ≤ G , 1\leq\Delta^{+}\leq\Delta\leq\mathbf{FN}_{p}(G)\leq\mathrm{nio}(G)\leq G, in which the various quotients of this series of groups are well understood. This sheds light on the ideal structure of the Iwasawa algebras (i.e. the completed group rings kG) of such groups, and will be used in future work to study the prime ideals of these rings.

Systematic review of universal school-based ‘resilience’ interventions targeting adolescent tobacco, alcohol or illicit substance use: A meta-analysis

Universal school-based interventions that address adolescent 'resilience' may represent a means of reducing adolescent substance use, however previous systematic reviews have not examined the effectiveness of such an intervention approach. A systematic review was undertaken to 1) assess whether universal school-based 'resilience' interventions are effective in reducing the prevalence of tobacco, alcohol or illicit substance use by adolescents, and 2) describe such effectiveness per intervention characteristic subgroups. Eligible studies were peer-reviewed reports (1994-2015) of randomised controlled trials including participants aged 5-18years that reported adolescent tobacco, alcohol or illicit substance use, and implemented a universal school-based 'resilience' intervention (i.e. those addressing both individual (e.g. self-esteem) and environmental (e.g. school connectedness) protective factors of resilience). Trial effects for binary outcomes were synthesised via meta-analyses and effect sizes reported as odds ratios. Subgroup (by intervention type, prevention approach, setting, intervention duration, follow-up length) and sensitivity analyses (excluding studies at high risk of bias) were conducted. Nineteen eligible studies were identified from 16,619 records (tobacco: n=15, alcohol: n=17, illicit: n=11). An overall intervention effect was found for binary measures of illicit substance use (n=10; OR: 0.78, 95%CI: 0.6-0.93, p=0.007,Tau2=0.0, I2=0%), but not tobacco or alcohol use. A similar result was found when studies assessed as high risk of bias were excluded. Overall intervention effects were evident for illicit substance use within multiple intervention characteristic subgroups, but not tobacco and alcohol. Such results support the implementation of universal school-based interventions that address 'resilience' protective factors to reduce adolescent illicit substance use, however suggest alternate approaches are required for tobacco and alcohol use. PROSPERO registration: CRD42014004906.

Use of BRCA Mutation Test in the U.S., 2004-2014.

BRCA mutation testing has been used for screening women at high risk of breast and ovarian cancer and for selecting the best treatment for those with breast cancer. To optimize the infrastructure and medical resources allocation for genetic testing, it is important to understand the use of BRCA mutation testing in the U.S. health system. This retrospective cohort study included 53,254 adult women with insurance claims for BRCA mutation testing between 2004 and 2014 from ClinformaticsTM Data Mart Database. Data analysis was performed in 2016. This study assessed trends in the use of BRCA mutation testing in women with previously diagnosed breast or ovarian cancer and those without (unaffected women). Between 2004 and 2014, of those receiving BRCA testing, the proportion of BRCA tests performed in unaffected women increased significantly (p<0.001), from 24.3% in 2004 to 61.5% in 2014. An increase in the proportion of BRCA tests used in unaffected women was found in each characteristic subgroup. In 2014, most subgroups had a proportion surpassing 50%, except for those aged 51-65 years and those without a family history of breast cancer. There was a much lower proportion of those aged 20-40 years among tested women with previously diagnosed breast or ovarian cancer than in unaffected women (17.6% vs 41.7%, p<0.001). During the past decade, the role of BRCA testing has gradually shifted from being used primarily in cancer patients to being used in unaffected women in the U.S.

Three-dimensional trajectories and network analyses of group behaviour within chimney swift flocks during approaches to the roost.

Chimney swifts (Chaetura pelagica) are highly manoeuvrable birds notable for roosting overnight in chimneys, in groups of hundreds or thousands of birds, before and during their autumn migration. At dusk, birds gather in large numbers from surrounding areas near a roost site. The whole flock then employs an orderly, but dynamic, circling approach pattern before rapidly entering a small aperture en masse. We recorded the three-dimensional trajectories of ≈1 800 individual birds during a 30 min period encompassing flock formation, circling, and landing, and used these trajectories to test several hypotheses relating to flock or group behaviour. Specifically, we investigated whether the swifts use local interaction rules based on topological distance (e.g. the n nearest neighbours, regardless of their distance) rather than physical distance (e.g. neighbours within x m, regardless of number) to guide interactions, whether the chimney entry zone is more or less cooperative than the surrounding flock, and whether the characteristic subgroup size is constant or varies with flock density. We found that the swift flock is structured around local rules based on physical distance, that subgroup size increases with density, and that there exist regions of the flock that are less cooperative than others, in particular the chimney entry zone.

Finite Groups and Lie Rings with an Automorphism of Order 2n

AbstractSuppose that a finite groupGadmits an automorphismof order 2nsuch that the fixed-point subgroupof the involutionis nilpotent of classc. Letm=) be the number of fixed points of. It is proved thatGhas a characteristic soluble subgroup of derived length bounded in terms ofn,cwhose index is bounded in terms ofm,n,c. A similar result is also proved for Lie rings.