有限群可解性的正规指数刻画

有限群可解性的正规指数刻画

魏先彪1,2;于力1

(1. 西安电子科技大学理学院, 陕西西安 710071;
2. 安徽建筑工业学院数理系, 安徽合肥 230022)

收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2004-04-20 发布日期:2004-04-20

On the solvability of finite groups based on normal indexes

WEI Xian-biao1,2;YU Li1

(1. School of Science, Xidian Univ., Xi'an 710071, China;
2. Dept. of Mathematics, Anhui Inst. of Architecture & Industry, Hefei 230022, China)

Received:1900-01-01 Revised:1900-01-01 Online:2004-04-20 Published:2004-04-20

摘要/Abstract

摘要： 有限群G的极大子群M的正规指数是指G的主因子H/K的阶，其中H为M在G中的极小正规补．文中利用正规指数的概念刻画有限群的可解性，给出了有限群可解的几个充分条件．

关键词: 有限群, 可解群, 正规指数

Abstract: For a maximal subgroup M of a finite group G, the normal index of M is defined as the order of a chief factor H/K, where H is minimal normal supplements of M in G. In this paper some sufficient conditions for solvability of finite groups are obtained by using the normal indexes of maximal subgroups.

Key words: finite group, solvable group, normal index

中图分类号:

O152.1

魏先彪1;2;于力1. 有限群可解性的正规指数刻画[J]. J4, 2004, 31(2): 300-303.

WEI Xian-biao1;2;YU Li1.

On the solvability of finite groups based on normal indexes

[J]. J4, 2004, 31(2): 300-303.