On non-Frattini chief factors and solvability of finite groups
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- 作者：JIANJUN LIU (1) liujj198123@163.com
XIUYUN GUO (2)
QIANLU LI (3) - 关键词：Frattini chief factors – ; solvable groups – ; semi cover ; avoiding properties
- 刊名：Proceedings Mathematical Sciences
- 出版年：2012
- 出版时间：May 2012
- 年：2012
- 卷：122
- 期：2
- 页码：163-173
- 全文大小：202.0 KB
- 参考文献：1. Ballester-Bolinches A and Ezquerro L M, Classes of finite groups (Dordrecht: Springer) (2006)
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- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Mathematics - 出版者：Springer India
- ISSN：0973-7685
文摘
A subgroup H of a group G is said to be a semi CAP *-subgroup of G if there is a chief series 1 = G 0 < G 1 < ⋯ < G m = G of G such that for every non-Frattini chief factor G i /G i − 1, H either covers G i /G i − 1 or avoids G i /G i − 1. In this paper, some sufficient conditions for a normal subgroup of a finite group to be solvable are given based on the assumption that some maximal subgroups are semi CAP *-subgroups.