关于李世荣的一个定理  

ON ONE OF LI SHIRONG'S THEOREM

作　　者：黎先华 

机构地区：[1]贵州师大数学系,贵阳550001

出　　处：《贵州师范大学学报（自然科学版）》1991年第3期18-22,共5页Journal of Guizhou Normal University：Natural Sciences

摘　　要：本文使用文献[1]的结果,证明了下列定理:定理设G为有限群。假若G的非正规极大子群同阶类类数=2,则(1)若G可解,则|π(r_∞(G))|≤2。(2)若G不可解,则其中Z_2~3为G′φ(G)的极小正规子群,K可解,i=0,1,2,……In this paper, We use the result of [1] to prove the following theorem: Theorem Let G be a finite group.If G has exactiy 2 the same order classes of maximal non-normal subgroups, then (1) If G is solvable, then |π(r_∞(G))| ≤2 (2) If G is non-solvable, then Where Z_2~3 is a minimal normal subgroup of G/φ(G), K is solvable group, i=0,1, 2,….

关 键 词：有限群论 同阶类 半直积 幂零剩余 

分 类 号：O152.1[理学—数学]