Group FH Research Articles

The Modular Isomorphism Problem – the alternative perspective on counterexamples

As a result of impressive research [5], D. García-Lucas, Á. del Río and L. Margolis defined an infinite series of non-isomorphic 2-groups G and H, whose group algebras FG and FH over the field F=F2 are isomorphic, solving negatively the long-standing Modular Isomorphism Problem (MIP). In this note we give a different perspective on their examples and show that they are special cases of a more general construction. We also show that this type of construction for p>2 does not provide a similar counterexample to the MIP.

On the modular isomorphism problem for groups of nilpotency class 2 with cyclic center

Abstract We show that the modular isomorphism problem has a positive answer for groups of nilpotency class 2 with cyclic center, i.e., that for such p-groups G and H an isomorphism between the group algebras FG and FH implies an isomorphism of the groups G and H for F the field of p elements. For groups of odd order this implication is also proven for F being any field of characteristic p. For groups of even order we need either to make an additional assumption on the groups or on the field.

Assessment of Patellar Morphology in Trochlear Dysplasia on Computed Tomography Scans.

ObjectiveTo evaluate the patellar morphology of trochlear dysplasia and normal knees in different genders and in different severities of trochlear dysplasia on CT scans.MethodsA total of 75 patients with trochlear dysplasia (110 knees) treated at the Third Hospital of Hebei Medical University from December 2013 to December 2018 were included in an experimental group, and an age‐matched and sex‐matched cohort of 46 patients with normal trochlear shape (61 knees) were randomly selected into a control group. The experimental group was divided into a female experimental group (Group FE, 47 patients, 72 knees) and a male experimental group (Group ME, 28 patients, 38 knees); the control group was divided into a female control group (Group FC, 31 knees, 24 female patients) and a male control group (Group MC, 30 knees, 22 male patients). Furthermore, according to the severity of trochlear dysplasia, Group FE was divided into a female low‐grade dysplasia group (Group FL, 20 knees) and a female high‐grade dysplasia group (Group FH, 52 knees); Group ME was divided into a male low‐grade dysplasia group (Group ML, 16 knees) and a male high‐grade dysplasia group (Group MH, 22 knees). All participants had undergone CT scans in the supine position; the patellar width and thickness, the lateral patellar facet angle, the Wiberg angle, and the Wiberg index were measured and compared.ResultsIn trochlear dysplasia knees, the mean patellar width and thickness and the lateral patellar facet angle were significantly smaller; the mean Wiberg index was significantly larger than in normal knees, regardless of gender (P < 0.05); and there was no statistically significant difference in the mean Wiberg angle (P > 0.05). In the female groups, the mean patellar width and thickness and the Wiberg angle were significantly smaller; the mean lateral patellar facet angle was significantly larger than those in the male groups (P < 0.05); and there was no significant difference in the mean Wiberg index (P > 0.05). In the low‐grade dysplasia group, the mean Wiberg index was smaller than that in the high‐grade dysplasia group (P < 0.05), regardless of gender; however, there was no significant difference in the mean patellar width and thickness, the lateral patellar facet angle, and the Wiberg angle in low‐grade and high‐grade dysplasia (P > 0.05).ConclusionOn CT scans, the patella in trochlear dysplasia had a smaller width, a thinner thickness, a lengthened lateral facet, and a more flattened articular facet. In addition, the patellar articular facet was more prominent in female patients. With the severity of trochlear dysplasia increased, the lateral patellar facet became longer. In addition, the abnormal stress distribution on the patella influenced the patellar morphology in trochlear dysaplasia.

Reduced Surgical Time and Higher Accuracy of Distal Locking with the Electromagnetic Targeting System in Humeral Shaft Intramedullary Nailing.

ObjectiveTo evaluate the efficacy of the electromagnetic distal targeting system in the treatment of humeral shaft fractures.MethodsFrom January 2012 to December 2018, we retrospectively reviewed 60 patients with humeral shaft fractures treated by intramedullary nailing. Among 60 cases, 41 were men and 19 were women. The average age at surgery was 48.5 years (range, 21–81 years). We performed the same surgical procedure for all patients. According to the different distal locking technique used, all patients were divided into two groups. The standard fluoroscopic freehand technique was used for Group FH, while the electromagnetic real‐time targeting technique was used for Group EM. All procedures were performed by two senior surgeons. Overall surgical time, cases of complications, failure of distal locking, union time, and shoulder function assessment were recorded intraoperatively and during follow‐up.ResultsTwenty‐seven patients in Group FH and 33 patients in Group EM met the inclusion criteria. No significant difference was found in the demographic data of the two groups. The mean surgical time was 76.48 ± 10.73 min in Group FH and 65.61 ± 8.91 min in Group EM (P < 0.05), showing significant difference. Seven failures occurred in Group FH and two failures occurred in Group EM (P < 0.05). No relevant complications were noted. The average union time was 3.37 ± 0.49 months in Group FH and 3.39 ± 0.50 months in Group EM (P = 0.855). The mean follow‐up was 14.30 ± 2.28 months in Group FH and 15.27 ± 2.83 months in Group EM (P = 0.153). The disabilities of the arm, shoulder and hand score (DASH) score, the range of motion (checked with the constant score), and the degree of functionality were, respectively, 21.52 ± 3.23, 27.04 ± 1.84, and 81.31% ± 3.88% in Group FH and 19.09 ± 2.40, 26.18 ± 1.70, and 77.97% ± 3.91% in Group EM (P = 0.233, 0.971, and 0.607).ConclusionThe electromagnetic real‐time targeting system reduced surgical time and improved accuracy, and there was no radiation exposure in the distal locking procedure for humeral shaft fractures.

On the nilpotency class of finite groups with a Frobenius group of automorphisms

Suppose that a metacyclic Frobenius group FH, with kernel F and complement H, acts by automorphisms on a finite group G, in such a way that C_G(F) is trivial and C_G(H) is nilpotent. It is known that G is nilpotent and its nilpotency class can be bounded in terms of |H| and the nilpotency class of C_G(H). Until now, it was not clear whether the bound could be made independent of the order of H. In this article, we construct a family mathfrak {G} of finite nilpotent groups, of unbounded nilpotency class. Each group in mathfrak {G} admits a metacyclic Frobenius group of automorphisms such that the centralizer of the kernel is trivial and the centralizer of the complement is abelian. This shows that the dependence of the bound on the order of H is essential.

Groups of automorphisms with TNI-centralizers

A subgroup H of a finite group G is called a TNI-subgroup if NG(H)∩Hg=1 for any g∈G\\NG(H). Let A be a group acting on G by automorphisms where CG(A) is a TNI-subgroup of G. We prove that G is solvable if and only if CG(A) is solvable, and determine some bounds for the nilpotent length of G in terms of the nilpotent length of CG(A) under some additional assumptions. We also study the action of a Frobenius group FH of automorphisms on a group G if the set of fixed points CG(F) of the kernel F forms a TNI-subgroup, and obtain a bound for the nilpotent length of G in terms of the nilpotent lengths of CG(F) and CG(H).

On the influence of fixed point free nilpotent automorphism groups

A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that \( [F,h]=F\) for all nonidentity elements \(h\in H\). Let FH be a Frobenius-like group with complement H of prime order such that \(C_F(H)\) is of prime order. Suppose that FH acts on a finite group G by automorphisms where \( (|G|,|H|)=1\) in such a way that \(C_G(F)=1.\) In the present paper we prove that the Fitting series of \(C_G(H)\) coincides with the intersections of \( C_G(H)\) with the Fitting series of G, and the nilpotent length of G exceeds the nilpotent length of \(C_G(H)\) by at most one. As a corollary, we also prove that for any set of primes \(\pi \), the upper \(\pi \)-series of \( C_G(H)\) coincides with the intersections of \(C_G(H)\) with the upper \(\pi \) -series of G, and the \(\pi \)- length of G exceeds the \(\pi \)-length of \( C_G(H)\) by at most one.

Pre-emptive administration of intravenous acetaminophen with transversus abdominis plane block (tap-blocke) in the prevention of fentanil-induced hyperalgesia in pediatric oncological patient undergoing abdominal surgery

Dmytriiev Dmytro, Nazarchuk Oleksandr. Pre-emptive administration of intravenous acetaminophen with transversus abdominis plane block (tap-blocke) in the prevention of fentanil-induced hyperalgesia in pediatric oncological patient undergoing abdominal surgery. Journal of Education, Health and Sport. 2015;5(10):98-107. ISSN 2391-8306. DOI http://dx.doi.org/10.5281/zenodo.32514 http://ojs.ukw.edu.pl/index.php/johs/article/view/2015%3B5%2810%29%3A98-107 https://pbn.nauka.gov.pl/works/659929 Formerly Journal of Health Sciences. ISSN 1429-9623 / 2300-665X. Archives 2011–2014 http://journal.rsw.edu.pl/index.php/JHS/issue/archive Deklaracja. Specyfika i zawartośc merytoryczna czasopisma nie ulega zmianie. Zgodnie z informacją MNiSW z dnia 2 czerwca 2014 r., ze w roku 2014 nie bedzie przeprowadzana ocena czasopism naukowych; czasopismo o zmienionym tytule otrzymuje tyle samo punktow co na wykazie czasopism naukowych z dnia 31 grudnia 2014 r. The journal has had 5 points in Ministry of Science and Higher Education of Poland parametric evaluation. Part B item 1089. (31.12.2014). © The Author (s) 2015; This article is published with open access at Licensee Open Journal Systems of Kazimierz Wielki University in Bydgoszcz, Poland and Radom University in Radom, Poland Open Access. This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited. This is an open access article licensed under the terms of the Creative Commons Attribution Non Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted, non commercial use, distribution and reproduction in any medium, provided the work is properly cited. This is an open access article licensed under the terms of the Creative Commons Attribution Non Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted, non commercial use, distribution and reproduction in any medium, provided the work is properly cited. The authors declare that there is no conflict of interests regarding the publication of this paper. Received: 05.08.2015. Revised 05.09.2015. Accepted: 20.10.2015. UDC : 616-089.5-053.2 : 616-006 PRE-EMPTIVE ADMINISTRATION OF INTRAVENOUS ACETAMINOPHEN WITH TRANSVERSUS ABDOMINIS PLANE BLOCK (TAP-BLOCKE) IN THE PREVENTION OF FENTANIL-INDUCED HYPERALGESIA IN PEDIATRIC ONCOLOGICAL PATIENT UNDERGOING ABDOMINAL SURGERY Dmytro Dmytriiev, Oleksandr Nazarchuk Department of Anesthesiology and Intensive care, Vinnytsya National Pirogov Memorial Medical University Abstract Background: Acetaminophen is a selective COX-2 agonist that has been shown to decrease the intensity of opioid-induced hyperalgesia (OIH) in children. We aimed to investigate the effects of preemptive administration of intravenous acitomenofen in the prevention of high-dose fentanil -induced hyperalgesia in pediatric patients. Methods : 45 patients of American Society of Anesthesiologists physical status 1-3 undergoing abdominal surgery were randomly assigned to one of the following three groups. each of which received either IV acetaminophen (an initial dose of 1.5 ml/kg for 40 min before before the induction of anesthesia) or placebo saline 40 min before the induction of anesthesia and intraoperative fentanil infusion: group LFH received a placebo and 0.05 μg/kg/min fentanil; group FH received a placebo and 0.3 μg/kg/min fentanil; and group AFH received IV preemptive administration acetaminophen and TAP-blocke bupivacaine 0,3 mg/kg. Results: The mechanical hyperalgesia threshold 12 hr after surgery was significantly lower in group FH than in the other two groups. Postoperative pain intensity using visual analog scale (VAS) and cumulative volume of a patient controlled analgesia (PCA) containing morphine over 12 hr were significantly greater in group FH than in group AFH. The time to the first postoperative analgesic requirement was significantly shorter in group RH than in the other two groups. The sevoflurane requirement was significantly greater in group LFH than in the other groups. The frequency of hypotension and bradycardia was significantly higher, but shivering and postoperative nausea and vomiting were significantly lower in group AFH than in the other two groups. Conclusions: High-doses of fentanil induced hyperalgesia, which presented a decreased mechanical hyperalgesia threshold, enhanced pain intensity, a shorter time to first postoperative analgesic requirement, and greater morphine consumption, but IV preemptive administration acetaminophen alleviated those symptoms. IV preemptive administration acetaminophen may be an effective treatment option for preventing or attenuating OIH. Key w ords: IV preemptive administration a cetaminophen, Opioid-induced hyperalgesia, fentanil , TAP-blocke.

Rank and Order of a Finite Group Admitting a Frobenius-Like Group of Automorphisms

A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that FH/[F,F] is a Frobenius group with Frobenius kernel F/[F,F]. Suppose that a finite group G admits a Frobenius-like group of automorphisms FH of coprime order with certain additional restrictions (which are satisfied, in particular, if either |FH| is odd or |H| = 2). In the case where G is a finite p-group such that G = [G, F] it is proved that the rank of G is bounded above in terms of |H| and the rank of the fixed-point subgroup C G (H), and that |G| is bounded above in terms of |H| and |C G (H)|. As a corollary, in the case where G is an arbitrary finite group estimates are obtained of the form |G| ≤|C G (F)| · f(|H|, |C G (H)|) for the order, and r(G) ≤ r(C G (F)) + g(|H|, r(C G (H))) for the rank, where f and g are some functions of two variables.

Derived length of a Frobenius-like kernel

A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F called kernel which has a nontrivial complement H such that FH/[F,F] is a Frobenius group with Frobenius kernel F/[F,F]. Suppose that a Frobenius-like group FH acts faithfully by linear transformations on a vector space V over a field of characteristic that does not divide |FH|. It is proved that the derived length of the kernel F is bounded solely in terms of the dimension m=dimCV(H) of the fixed-point subspace of H by g(m)=3+[log2(m+1)]. It follows that if a Frobenius-like group FH acts faithfully by coprime automorphisms on a finite group G, then the derived length of the kernel F is at most g(r), where r is the sectional rank of CG(H). As an application, for a finite solvable group G admitting an automorphism φ of prime order coprime to |G|, a bound for the p-length of G is obtained in terms of the rank of a Hall p′-subgroup of CG(φ). Earlier results of this kind were known only in the special case when the complement of the acting Frobenius-like group was assumed to have prime order and its fixed-point subspace (or subgroup) was assumed to be one-dimensional (or have all Sylow subgroups cyclic).

Nilpotent Length of a Finite Solvable Group with a Frobenius Group of Automorphisms

We prove that a finite solvable group G admitting a Frobenius group FH of automorphisms of coprime order with kernel F and complement H such that [G, F] = G and C C G (F)(h) = 1 for all nonidentity elements h ∈ H, is of nilpotent length equal to the nilpotent length of the subgroup of fixed points of H.

Action of a Frobenius-like group with fixed-point free kernel

Abstract We call a finite group Frobenius-like if it has a nontrivial nilpotent normal subgroup F possessing a nontrivial complement H such that [ F , h ] = F ${[ F,h] =F}$ for all nonidentity elements h ∈ H. We prove that any irreducible nontrivial F H-module for a Frobenius-like group F H of odd order over an algebraically-closed field has an H-regular direct summand if either F is fixed-point free on V or F acts nontrivially on V and the characteristic of the field is coprime to the order of F. Some consequences of this result are also derived.

Action of a Frobenius-like group

We call a finite group Frobenius-like if it has a nontrivial nilpotent normal subgroup F possessing a nontrivial complement H such that [F,h]=F for all nonidentity elements h∈H. We prove that any irreducible nontrivial FH-module for a Frobenius-like group FH of odd order over an algebraically closed field has an H-regular direct summand if either F is fixed point free on V or F acts nontrivially on V and the characteristic of the field is coprime to the order of F. Some consequences of this result are also derived.

Frobenius-like groups as groups of automorphisms

A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that FH/[F,F] is a Frobenius group with Frobenius kernel F/[F,F]. Such subgroups and sections are abundant in any nonnilpotent finite group. We discuss several recent results about the properties of a finite group G admitting a Frobenius-like group of automorphisms FH aiming at restrictions on G in terms of C_G(H) and focusing mainly on bounds for the Fitting height and related parameters. Earlier such results were obtained for Frobenius groups of automorphisms; new theorems for Frobenius-like groups are based on new representation-theoretic results. Apart from a brief survey, the paper contains the new theorem on almost nilpotency of a finite group admitting a Frobenius-like group of automorphisms with fixed-point-free almost extraspecial kernel.

Rank and Order of a Finite Group Admitting a Frobenius Group of Automorphisms

Suppose that a finite group G admits a Frobenius group FH of automorphisms of coprime order with kernel F and complement H. For the case where G is a finite p-group such that G = [G, F], it is proved that the order of G is bounded above in terms of the order of H and the order of the fixed-point subgroup C G (H) of the complement, while the rank of G is bounded above in terms of |H| and the rank of C G (H). Earlier, such results were known under the stronger assumption that the kernel F acts on G fixed-point-freely. As a corollary, for the case where G is an arbitrary finite group with a Frobenius group FH of automorphisms of coprime order with kernel F and complement H, estimates are obtained which are of the form |G| ≤ |C G (F)| · f(|H|, |C G (H)|) for the order, and of the form r(G) ≤ r(C G (F)) + g(|H|, r(C G (H))) for the rank, where f and g are some functions of two variables.

Fixed points of Frobenius groups of automorphisms

A finite group admits a Frobenius automorphisms group FH with a kernel and complement H such that the fixed-point subgroup of F is trivial. It is further proved that every FH-invariant elementary Abelian section of G is a free module for an appropriate prime p. The exponent of a group is bounded with a metacyclic Frobenius group of automorphisms and it is supposed that a finite Frobenius group FH with cyclic kernel F and complement H acts on a finite group G. Bounds for the nilpotency class of groups and Lie rings admitting a metacyclic Frobenius group of automorphisms with fixed-point free kernel are obtained. It is also found that a locally nilpotent torsion-free group G admits a finite Frobenius group of automorphisms FH with cyclic kernel F and complement H of order q.

Nilpotent length of a finite group admitting a frobenius group of automorphisms with fixed-point-free kernel

Suppose that a finite group G admits a Frobenius group FH of automorphisms with kernel F and complement H such that the fixed-point subgroup of F is trivial, i.e., CG(F) = 1, and the orders of G and H are coprime. It is proved that the nilpotent length of G is equal to the nilpotent length of CG(H) and the Fitting series of the fixed-point subgroup CG(H) coincides with a series obtained by taking intersections of CG(H) with the Fitting series of G.

On the exponent of a finite group with an automorphism group of order twelve

Suppose that a Frobenius group FH with kernel F of order 4 and complement H of order 3 acts coprimely on a finite group G in such a manner that C G ( F ) = 1 and C G ( H ) has exponent e. We prove that the exponent of G is e-bounded. Earlier results of this nature were known only for metacyclic Frobenius groups.

Higher levels of central adiposity in healthy premenopausal women with family histories of premenopausal breast cancer

Research strongly suggests that lower overall adiposity and higher central adiposity are independent risk factors for premenopausal breast cancer in the general population. We aimed to test the possibility that these factors may contribute to familial risk of premenopausal breast cancer. A convenience sample of healthy women, ages 25-49, was recruited to yield three study groups: (1) Women with first-degree family histories of premenopausal breast cancer, operationally defined as being diagnosed prior to age 50 (Group FH < 50, n = 39); (2) Women with first-degree family histories of postmenopausal breast cancer, operationally defined as being diagnosed at age 50 or after (Group FH > or = 50, n = 33); and (3) Women without a history of breast cancer in first-degree relatives (Group FH-, n = 132). Multinomial logistic regression analyses, including possible confounders, waist circumference, and BMI, revealed a lower BMI among FH < 50 compared to either FH- (OR = 0.72; 95% CI = 0.59-0.87), or FH > or = 50 women (OR = 0.75; 95% CI = 0.60-0.95), and higher waist circumferences in FH < 50 compared to either FH- (OR = 1.15; 95% CI = 1.06-1.25), or FH > or = 50 women (OR = 1.16; 95% CI = 1.05-1.28). No group differences were seen for waist skinfold measures. These results support the possibility that differences in patterns of adiposity may contribute to familial risk of premenopausal breast cancer, and suggest the importance of conducting large scale, population-based studies of the link between body size characteristics and familial breast cancer risk.

Combined Treatment With Sustained-Release Basic Fibroblast Growth Factor and Heparin Enhances Neovascularization in Hypercholesterolemic Mouse Hindlimb Ischemia

Whether the combined treatment with sustained-release basic fibroblast growth factor (bFGF) and heparin enhances neovascularization in hypercholesterolemic mouse hindlimb ischemia was investigated. Wild-type C57BL/6 and low density lipoprotein receptor-deficient mice were assigned to 1 of the following 4 experimental groups and treated for 2 weeks after femoral artery extraction: group N, no treatment; group H, daily subcutaneous injection of heparin calcium; group F, single intramuscular injection of the sustained-release bFGF microspheres; and group FH, combined treatment with sustained-release bFGF and heparin. Among the wild-type mice at 4 weeks after femoral artery extraction, the laser Doppler perfusion image index (LDPII) in groups H, F, and FH was significantly higher than that in group N. The vascular density in group FH was the highest among the 4 groups. The maturation index in the 3 treated groups was significantly higher than that in group N. Among the hypercholesterolemic mice, the LDPII in group FH was significantly higher than that in the other 3 groups. The vascular density and maturation index in group FH were the highest among the 4 groups. Combined treatment with sustained-release bFGF and heparin enhanced neovascularization in the hypercholesterolemic hindlimb ischemia model.