三阶整系数矩阵群的极大有限子群

利用Date给出的方法将 3阶整系数矩阵群的所有极大有限子群进行分类 ,所得的结果是存在 4个算术等价类 ,2个几何等价类 ,对每一个等价类我们给出一个群作为代表元 .

Finite groups whose maximal subgroups of sylow p-subgroups admit a p-solvable supplement

In this note,we show that if every maximal subgroup of a Sylow p-subgroup of a finite group has a p-solvable supplement then the group is necessarily p-solvable.This gives a positive answer to Problem 17.111 of the Kourovka Notebook(Unsolved Problems in Group Theory),which was posed by Skiba.

Finite groups with systems of Σ-embedded subgroups

In recent years,a series of papers about cover-avoiding property of subgroups appeared and all the studies were connected with chief factors of a finite group.However,about the cover-avoiding property of subgroups for non-chief factor,there is no study up to now.The purpose of this paper is to build the theory.Let A be a subgroup of a finite group G and Σ:G0≤G1≤…≤Gn some subgroup series of G.Suppose that for each pair(K,H) such that K is a maximal subgroup of H and G i 1 K < H G i for some i,either A ∩ H = A ∩ K or AH = AK.Then we say that A is Σ-embedded in G.In this paper,we study the finite groups with given systems of Σ-embedded subgroups.The basic properties of Σ-embedded subgroups are established and some new characterizations of some classes of finite groups are given and some known results are generalized.

Finite p-Groups all of Whose Maximal Subgroups Either are Metacyclic or Have a Derived Subgroup of Order ≤ p

The groups as mentioned in the title are classified up to isomorphism. This is an answer to a question proposed by Berkovich and Janko.

Finite Groups All of Whose Second Maximal Subgroups Are PSC*-Groups

This paper discusses the influence of minimal subgroups on the structure of finite groups and gives the structures of finite groups all of whose second maximal subgroups are PSC*-groups.