对于某些素数共轭类长无立方因子的有限群

G是有限群。Con（G）表示G的所有共轭类组成的集合。考虑了具有GN（p）性质的有限群G：对于群阶的某一素因子,C的共轭类长无立方嘶因子,目的是研究共轭类的长对群的结构的影响。由此得到结果中的两个结论在某种附加条件下推广了D．Chillag和M．Herzog关于共轭类长的两个结果。     

L2（q）的一个特征性质

本文证明了下述结果:如G是有限群且对每个质数r都有|N_G(R_1)_=|N_(L_(2(q)))(R_2)|,那么GL_2(q),此处R_1∈SyI_ΓG,R_2∈SyI_Γ(L_2(q))。     

The average number of Sylow subgroups of a finite group

We prove that if the average Sylow number (ignoring the Sylow numbers that are one) of a finite group G is ?7, then G is solvable.     

极大子群的θ-偶与群的可解性

利用有限群极大子群的极大θ-偶的性质,在限制条件较相关文献弱的情形下,研究群的可解性.     

与有限单群R(q)有相同Sylow正规化子阶的有限群

在这篇文章中,作者证明:有限群G同构于R(32m+1)(m＞0)当且仅当,对每个素数r,它们有相同的Sylow r-正规化子的阶.     

Locally Transitive Graphs Admitting a Group with Cyclic Sylow Subgroups

All graphs are finite simple undirected and of no isolated vertices in this paper. Using the theory of coset graphs and permutation groups, it is completed that a classification of locally transitive graphs admitting a non-Abelian group with cyclic Sylow subgroups. They are either the union of the family of arc-transitive graphs, or the union of the family of bipartite edge-transitive graphs.     

G-covering systems of subgroups for the class of supersoluble groups

Let ? be a class of groups. Given a group G, assign to G some set of its subgroups Σ = Σ(G). We say that Σ is a G-covering system of subgroups for ? (or, in other words, an ?-covering system of subgroups in G) if G ∈ ? wherever either Σ = ? or Σ ≠ ? and every subgroup in Σ belongs to ?. In this paper, we provide some nontrivial sets of subgroups of a finite group G which are G-covering subgroup systems for the class of supersoluble groups. These are the generalizations of some recent results, such as in [1–3].     

素数幂阶子群的s-半置换性对有限群结构的影响

设G为有限群,G的一个子群H称为半置换的,若对任意的K≤G,只要(|K|,|H|)=1,就有KH=HK;H称为s-半置换的,若对任意的p||C|,只要(p,|H|)=1,就有PH=HP,其中P∈Sylp(G).本文考察了素数幂阶子群的s-半置换性对有限群的超可解性的影响.     

有限单群O_(2n)~-(2)(4≤n≤6)的一个特征性质

设G为有限群 ,H为下述单群之一 :O-8(2 ) ,O-1 0 (2 ) ,O-1 2 (2 ) .在这篇文章中 ,证明了G H当且仅当对每个质数r,它们有相同的Sylowr-正规化子的阶 .     

Automorphisms and normal subgroups of linear groups

In the present paper, the properties of orders of coprime automorphisms of irreducible linear groups are established and sufficient conditions for the existence of a normal Hall π-subgroup in a given π-separable irreducible complex linear group are obtained. Библиография: 11 наэваний.