2-极大子群次正规的有限群的一个注记

郭鹏飞

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2-极大子群次正规的有限群的一个注记

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- 2-极大子群次正规的有限群的一个注记
- 2-极大子群次正规的有限群的一个注记
- Issue 2, (2006)
- 作者机构：
  
  山西师范大学数学与计算机科学学院
- 作者简介：
- 基金信息：
- DOI：
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- Published：2006
- 稿件说明：
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郭鹏飞. 2-极大子群次正规的有限群的一个注记[J]. 2006, (2).
DOI：

郭鹏飞. 2-极大子群次正规的有限群的一个注记[J]. 2006, (2). DOI：

摘要

设H是有限群G的一个子群

若存在G的极大子群K

使得H是K的极大子群

则称H为G的一个2-极大子群.本文考查了群G的所有2-极大子群均在G中次正规时对有限群G结构的影响

得到内幂零群为超可解群的两个充分条件;当G的F rattin i子群为1时

考虑F(G)的所有极小子群均在G中正规及群G阶的素因子之间的关系

得到群G幂零的一个充分条件.

Abstract

A subgroup H of a finite group G is said to be 2-maximal subgroup in G if there is a subgroup K which is a maximal subgroup of G such that H is a maximal subgroup of K.After taking into account of the impact of all the subnormal 2-maximal subgroups in G on the structure of the finite group G

the author has obtained two sufficient conditions for finite minimal non-nilpotent groups to be super-solvable

and obtained a sufficient condition for finite groups to be nilpotent by taking into account of the fact that every minimal subgroup of F(G) is normal in G and of the relationship of the prime divisors of ｜G｜ while Ф(G)=1.

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