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1.
本文主要讨论欧氏整环上线性群一类子群的结构,并获得其一类极大子群, 相似文献
2.
关于有限群的$CAP$-嵌入子群 总被引:1,自引:0,他引:1
A subgroup H of a finite group G is said to be CAP-embedded subgroup of G if, for each prime p dividing the order of H, there exists a CAP-subgroup K of G such that a Sylow p-subgroup of H is also a Sylow p-subgroup of K. In this paper some new results are obtained based on the assumption that some subgroups of prime power order have the CAP-embedded property in the group. 相似文献
3.
In this paper it is proved that the set of primitive elements of a non-Abelian free group has density zero, i.e. the ratio of primitive elements in increasingly large balls is arbitrarily small. Two notions of density (natural and exponential density) are defined and some of their properties are studied. A class of subsets of the free group (graphical sets) is defined restricting the occurrence of adjacent letters in the reduced word for an element, and the relation between graphical sets and the set of primitive elements is studied and used to prove the above result. 相似文献
4.
U. Dempwolff 《Designs, Codes and Cryptography》2001,22(2):191-207
We determine the symmetric designs
which admit a group
such that G has a nonabelian socle and is a primitiverank 3 group on points (and blocks). 相似文献
5.
G. N. Arzhantseva 《Geometriae Dedicata》2001,87(1-3):191-208
We prove that a quasiconvex subgroup H of infinite index of a torsion free word hyperbolic group can be embedded in a larger quasiconvex subgroup which is the free product of H and an infinite cyclic group. Some properties of quasiconvex subgroups of word hyperbolic group are also discussed. 相似文献
6.
有限群极大子群的θ-子群偶 总被引:21,自引:0,他引:21
N.P.Mukherjee和 P.Bhattacharya在“On theta pairs for a maximal sub-group”(Proc.Amer.Math.Soc,Vl09N3(1990))一文中定义了有限群的极大子群的θ-子群偶概念,研究了极大子群的极大θ-子群偶对群结构的影响,得到了一系列结果.本文在进一步探究θ-子群偶性质的基础上,对该文中一系列主要结果作出了本质性的改进,并给出了可解性、幂零性的一些新刻划. 相似文献
7.
In the present paper, for any finite group G of Lie type (except for 2
F
4(q)), the order a(G) of its large Abelian subgroup is either found or estimated from above and from below (the latter is done for the groups F
4
(q), E
6
(q), E
7
(q), E
8
(q), and 2
E
6(q
2)). In the groups for which the number a(G) has been found exactly, any large Abelian subgroup coincides with a large unipotent or a large semisimple Abelian subgroup. For the groups F
4
(q), E
6
(q), E
7
(q), E
8
(q), and 2
E
6(q
2)), it is shown that if an Abelian subgroup contains a noncentral semisimple element, then its order is less than the order of an Abelian unipotent group. Hence in these groups the large Abelian subgroups are unipotent, and in order to find the value of a(G) for them, it is necessary to find the orders of the large unipotent Abelian subgroups. Thus it is proved that in a finite group of Lie type (except for 2
F
4(q))) any large Abelian subgroup is either a large unipotent or a large semisimple Abelian subgroup. 相似文献
8.
9.
10.
Paul Schmutz Schaller 《Compositio Mathematica》2000,122(3):243-260
Let M be a hyperbolic surface and (M) its extended mapping class group. We show that (M) is isomorphic to the automorphism group of the following graph G(M). The set of vertices of G(M) is the set S(M) of nonseparating simple closed geodesics of M. Two vertices u and v of S(M) are related by an edge if u and v intersect exactly once in M. The graph G(M) can be thought of as a combinatorial model for M. 相似文献
11.
Let G be a finite group and δ(G) denote the number of conjugacy classes of all non-cyclic subgroups of G. The symbol π(G) denotes the set of the prime divisors of |G|. In [7], Meng and Li showed the inequality δ(G)≥2|π(G)|?2, where G is non-cyclic solvable group. In this paper, we describe the finite groups G such that δ(G) = 2|π(G)|?2. Another aim of this paper would show δ(G)≥M(G)+2 for unsolvable groups G and the equality holds ?G?A5 or SL(2,5), where M(G) denotes the number of conjugacy classes of all maximal subgroups of G. 相似文献
12.
Some Groups Having Only Elementary Actions on Metric Spaces with Hyperbolic Boundaries 总被引:1,自引:0,他引:1
We study isometric actions of certain groups on metric spaces with hyperbolic-type bordifications. The class of groups considered includes SL
n
(), Artin braid groups and mapping class groups of surfaces (except the lower rank ones). We prove that in various ways such actions must be elementary. Most of our results hold for non-locally compact spaces and extend what is known for actions on proper CAT(-1) and Gromov hyperbolic spaces. We also show that SL
n
() for n 3 cannot act on a visibility space X without fixing a point in
. Corollaries concern Floyd's group completion, linear actions on strictly convex cones, and metrics on the moduli spaces of compact Riemann surfaces. Some remarks on bounded generation are also included. 相似文献
13.
s-半置换子群对有限群的p-超可解性的影响 总被引:1,自引:0,他引:1
群G的子群H称为半置换的,若对任意的K≤G,只要(|H|,|K|)=1,就有HK=KH.H称为s-半置换的,若对任意的p||G|,只要(p,|H|)=1,就有PH=HP,其中P∈Sylp(G).本文研究Sylow子群的极大子群及极小子群的s-半置换性对有限群的p-超可解性的影响. 相似文献
14.
群G的子群H称为G的CAP-嵌入子群,如果对于|H|的每个素因子p,存在G的某个CAP-子群K,使得H的某个Sylow p-子群也是K的一个Sylowp-子群.本文通过假定G的p-Fitting子群F_p(G)的某个Sylow p-子群的每个极大子群是G的CAP-嵌入子群,得到一些新的结果. 相似文献
15.
对特征不为2的任意域上Ci型Chevaley群,构造了一类真包含单项子群的子群,从而否定回答子单项子群的极大性问题,同时证明了所构造的群恰为极大子群。 相似文献
16.
群G的子群H称为半置换的,若对任意的K≤G,只要(|H|,|K|)=1.就有HK=KH,H称为s-半置换的,若对任意的p‖G|,只要(p,|H|)=1,就有PH=HP,其中P∈Sylp(G).本文利用Sylow子群的2-极大子群的s-半置换性得到有限群为p-幂零群的一些充分条件. 相似文献
17.
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
18.
In this article we use the Classification of the Finite Simple Groups, the O'Nan–Scott Theorem, and Aschbacher's theorem to classify the primitive permutation groups of degree less than 4096. The results will be added to the primitive groups databases of GAP and MAGMA. 相似文献
19.
A subgroup of a group G is said to be Sylow-quasinormal (S-quasinormal) in G if it permutes with every Sylow subgroup of G. A subgroup H of a group G is said to be Supplement-Sylow-quasinormal (SS-quasinormal) in G if there is a supplement B of H to G such that H is permutable with every Sylow subgroup of B. In this article, we investigate the influence of SS-quasinormal of maximal or minimal subgroups of Sylow subgroups of the generalized Fitting subgroup of a finite group. 相似文献
20.