proper subgroup meaning in English
真子群
Examples
- Theorem 2 . 4 let g be a non - abelian inner - finite group , each non - trivial proper subgroup of g is prime order cyclic group if and only if g is a simple group ; each proper subgroup of g is nilpotent ; and each non - trivial subgroup of g is self - normalizer
4设g是非阿贝尔的内有限群，则g的每个非平凡真子群都是素数阶循环群的充分必要条件是g是单群， g的每个真子群幂零且g的每个非平凡的真子群自正规化定理2 - It is important to study the structures of finite groups by combining some subgroups with some properties in the researches on finite groups . in this paper , we discuss the following : ( 1 ) the relations between the - pairs of maximal subgroups and c - normality , weak c - normality , s - normality , the normal index of maximal subgroups ; ( 2 ) some results on solvablity of finite groups that are obtained by using the s - normality of subgroups ; ( 3 ) the - pairs of general proper subgroups of finite groups as the generalization of the - pairs of maximal subgroups that is used to describe c - normal subgroups , weak c - normal subgroups and s - normal subgroups , by which some new results on finite groups are obtained ; ( 4 ) some new results on p - quasinilpotent groups and p * - nilpotent groups
本文在前人的基础上，讨论了以下内容： ( 1 )极大子群的子群偶和c正规性、弱c正规性、 s正规性、正规指数之间的关系； ( 2 )利用s正规性得到了关于有限群可解性的几个结果； ( 3 )将极大子群的子群偶推广为有限群的一般真子群的偶，证明了有限群的c正规、弱c正规以及s正规子群都可以用一般真子群的偶来描述和几个新的结果； ( 4 )研究p拟幂零群和p ~ *幂零群，得到了一些新的结构定理。 - Theorem 2 . 5 let g be an infinite simple group that satisfies maximal condition . g is an inner - finite group and each non - trivial proper subgroup of g is abelian if and only if for each x in g , cg ( x ) is the only maximal subgroup that contain x . s * ( a * , c * ) - groups can be regarded as a generalizations of dedekind groups , since all of dedekind groups are s * ( a * , c * ) - groups
5设g是满足极大条件的无限单群，则g是内有限群，而且g的每个非平凡真子群是阿贝尔群的充分必要条件是对g的任意非平凡元x ，有c _ g ( x )是g的含x的唯一极大子群且c _ g ( x )是有限的。