非幂零真子群同阶类类数给定的有限群  

Finite Groups in Which the Number of Classes of Non-nilpotent Proper Subgroups of the Same Order is Given

作　　者：史江涛[1] 张翠 

机构地区：[1]烟台大学数学与信息科学学院,山东烟台264005 [2]Faculty of Mathematics,Natural Sciences and Information Technologies,University of Primorska,Glagoljaska 8,6000 Koper,Slovenia [3]Primorska Institute of Natural Sciences and Technology,University of Primorska,Muzejski trg 2,6000 Koper,Slovenia

出　　处：《数学年刊（A辑）》2011年第6期687-692,共6页Chinese Annals of Mathematics

基　　金：中国博士后科学基金(No20100470136;No201104027);"Agencija za raziskovalno dejavnost Republike Slovenije";projmladi raziskovalci;"Agencija za raziskovalno dejavnost Republike Slovenije";research program P1-0285资助的项目

摘　　要：作为Schmidt定理的推广,证明了:(1)非幂零真子群同阶类类数<3的有限群可解;(2)G为非幂零真子群同阶类类数=3的非可解群当且仅当G≌A_5或G≌SL_2(5).此外,完全分类了非平凡幂零子群同阶类类数≤5的非可解群和非平凡子群同阶类类数≤9的非可解群.As an extension of Schmidt theorem,the following results are obtained：（1） A finite group with less than 3 classes of non-nilpotent proper subgroups of the same order is solvable;（2） G is a non-solvable group with exactly 3 classes of non-nilpotent proper subgroups of the same order if and only if G≌A_5 or G≌SL_2（5）.Furthermore,non-solvable groups with at most 5 classes of non-trivial nilpotent subgroups of the same order and non-solvable groups with at most 9 classes of non-trivial subgroups of the same order are completely classified.

关 键 词：非幂零子群 同阶类 可解群 

分 类 号：O152.1[理学—数学]