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本文讨论含指数为素数幂的超可解子群的有限群的结构.首先得到具有这种性质的非Abel有限单群的完全分类定理.其次给出了这类群是可解群和超可解群的若干充分条件. 相似文献
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有限群为超可解群的充要条件 总被引:1,自引:0,他引:1
用置换条件刻画有限可解群的超可解性已有大量结果,本文的目的是给出另外一些有限可解群为超可解的充要条件。其主要结果是: 1.设G是满足置换条件的有限可解群,则G是超可解群当且仅当如下条件之一成立。 1)G的2-Sylow子群G_2的换位子群G_2′G. 2)G有正规2-补。 2.设G是有限可解群,则G超可解当且仅当G和G′均满足置换条件. 相似文献
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一类2~3p~n(p=3,7)阶群的构造 总被引:2,自引:0,他引:2
本文利用超可解群的性质,通过群的扩张理论,利用一种新的证明方法解决了2~3p~n(p=3,7)阶群当sylow-p子群为循环群时的构造. 相似文献
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本文利用超可解群的性质,通过群的扩张理论,利用一种新的证明方法解决了2^3p^n(p=3,7)阶群当sylow-p子群来循环时的构造。 相似文献
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某些子群是半正规的有限群 总被引:6,自引:0,他引:6
本文旨在考查极大子群对有限群结构的影响.首先给出了商群超可解的群是超可解群的若干充分条件;其次考查了n-极大子群对有限群的可解性及超可解性的影响 相似文献
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超可解群的若干充分条件 总被引:9,自引:0,他引:9
本文研究了有限群的超可解性问题,利用子群的共轭可换性概念及极小反例法,获得了一个群为超可解的若干充分条件.举例说明了主要结果中的假设条件是不可少的. 相似文献
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刘合国 《数学年刊A辑(中文版)》1999,(4)
本文通过Baer的超可解性定理、证明了有限生成的超Abel群的两个超可解性条件,包含了Hup-pert和Baer关于有限超可解群的结果[3]. 相似文献
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本文首先将Hal定理推广为:设N为G的正规子群,若N为Enπ群,G/N为Dπ群,则G为Dπ群.在此基础上得到了群G为Enπ群的充要条件为:(1)G存在正规子群N,满足N及G/N为Enπ群;(2)对任意p∈π,任意q∈π {p}及任意p 元素x,CG(x)含G的Sylowq 子群.另外,我们对非Able单群的情形也进行了一些讨论. 相似文献
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Ann Kiefer 《代数通讯》2013,41(12):4408-4418
The number of pairs of commuting involutions in Sym(n) and Alt(n) is determined up to isomorphism. It is also proven that, up to isomorphism and duality, there are exactly two abstract regular polyhedra on which the group Sym(6) acts as a regular automorphism group. 相似文献
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A Garside group is a group admitting a finite lattice generating set
. Using techniques developed by Bestvina for Artin groups of finite type, we construct K(π, 1)s for Garside groups. This construction shows that the (co)homology of any Garside group G is easily computed given the lattice
, and there is a simple sufficient condition that implies G is a duality group. The universal covers of these K(π, 1)s enjoy Bestvina's weak nonpositive curvature condition. Under a certain tameness condition, this implies that every
solvable subgroup of G is virtually Abelian. 相似文献
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Jhoel S. Gutierrez 《代数通讯》2020,48(4):1510-1527
AbstractWe study homological approximations of the profinite completion of a limit group (see Thm. A) and obtain the analogous of Bridson and Howie’s Theorem for the profinite completion of a non-abelian limit group (see Thm. B). 相似文献
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《代数通讯》2013,41(5):1417-1425
ABSTRACT Let n be an integer greater than 1. A group G is said to be n-rewritable (or a Qn-group) if for every n elements x1, x2,…,xn in G there exist distinct permutations σ and τ in Sn such that xσ(1)xσ (2) ??? xσ(n) = xτ(1)xτ(2) ??? xτ(n). In this paper, we characterize all 3-rewritable nilpotent 2-groups of class 2. Also we have found a bound for the nilpotency class of certain nilpotent 3-rewritable groups, and have shown that 3-rewritable groups satisfy a certain law. 相似文献
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Let P be a Sylow p-subgroup of a group G with the smallest generator number d,where p is a prime.Denote by M_d(P) = {P_1,P_(2,...,)P_d} a set of maximal subgroups of P such that φ(P) = ∩_(n=1)~dP_n.In this paper,we investigate the structure of a finite group G under the assumption that the maximal subgroups in M_d(P) are weakly s-permutably embedded in G,some interesting results are obtained which generalize some recent results.Finally,we give some further results in terms of weakly s-permutably embedded subgroups. 相似文献
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Denote by ω(G) the number of orbits of the action of Aut(G) on the finite group G. We prove that if G is a finite nonsolvable group in which ω(G) ≤5, then G is isomorphic to one of the groups A5, A6, PSL(2, 7), or PSL(2, 8). We also consider the case when ω(G) = 6 and show that, if G is a nonsolvable finite group with ω(G) = 6, then either G ≈ PSL(3, 4) or there exists a characteristic elementary abelian 2-subgroup N of G such that G/N ≈ A5. 相似文献
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主要研究子群置换性质对有限群结构的影响.通过子群的置换性得到一类群,即B 群.B群是全可置换群的扩展,利用全可置换群的p次中心扩张和子群的阶得到B群的一些性质并对B 群的结构进行一些刻画.应用B 群的结构得到有限p (p〉2)群为二元生成的B 群的充要条件. 相似文献
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Using the canonical JSJ splitting, we describe the outer automorphism group Out(G) of a one-ended word hyperbolic group G. In particular, we discuss to what extent Out(G) is virtually a direct product of mapping class groups and a free abelian group, and we determine for which groups Out(G) is infinite. We also show that there are only finitely many conjugacy classes of torsion elements in Out(G), for G any torsion-free hyperbolic group. More generally, let Γ be a finite graph of groups decomposition of an arbitrary group G such that edge groups Ge are rigid (i.e. Out(Ge) is finite). We describe the group of automorphisms of G preserving Γ, by comparing it to direct products of suitably defined mapping class groups of vertex groups. 相似文献