The orders of automorphism groups of some families p-groups;
某一类家族p-群的自同构群的阶(英文)
The Order of Automorphism Group of One Special Family of p-Group;
一类特殊的p-群的自同构群的阶
The Orders of the Automorphism Groups of Some p-groups;
若干家族p-群的自同构群的阶
The paper show that the p-group G can be classified into 15 classes which are non-isomorphic each other, where G be of cycle centre, and G / Z(G) be of order p~5.
本文证明中心循环且中心商为p~5阶群的有限p群能分为15个互不同构的类。
In this paper,the authors give three groups of order p~6 with p-groups as auto- morphism groups,and obtain their orders of automorphism groups.
该文给出了三个以p群为自同构群的p~6阶群,并得到了它们的自同构群的阶。
Given a p-solvable group G and an irreducible Brauer character χ of G with respect to the prime p.
给定一个p-可解群G以及G的一个关于该素数p的不可约B rauer特征标χ。
Using the properties of solvable groups and the basic theorems of finite groups,and utilizing the partly analytical method,the properties of some subgroups of p-solvable groups and the action on subgroups are studied.
利用可解群的性质和有限群的基本定理,通过局部分析方法研究了p-可解群中一些子群的性质及子群间的相互作用,并着重考察了Op′(G)=1的情况,得到了关于p-可解群的一些结论。
In this paper we research the basic property and the action on subgroup of solvable groups,in p-solvable groups we especially consider it in the case O_(P )(G) = 1 in p-solvable groups.
本文考察了可解群的基本性质及一些子群的相互作用，在p-可解群中，着重考察了当O_(p′)(G)=1时的情况。
We now state Theorem 3 as follows:"Let G be nonabelian elementatry finite p-group(p prime,p≠2) with order p~4,and let H be N_p-series of G with t_1=3, t_2=1,c=2.
应用具有Np-序列有限p-群的特殊性质和重量函数,基本序列等概念以及已有的一些结果,分别研究了类为1的pk(k 2)阶A bel基本p-群和类为2的p4阶基本p-群之增广商群Qn(G)的结构,得到了当n足够大时Qn(G)作为A bel基本p-群的秩。
Let G be a finite p-group and M,N be two normal subgroups of G satisfying M ≤ N ∩ Z(G).
设G为有限p-群,M,N均为G的正规子群且M≤N∩Z(G),证明了CAutG(G/M,N)G≤N的充要条件是G′≤N,M为循环群且exp(G/N)≤expM。