Π-可补充子群对有限群结构的影响
The Influence of Π-Supplemented Subgroups on Finite Groups

作者: 李保军 , 刘阿明 :成都信息工程学院应用数学学院,成都;

关键词: 有限群p-幂零&Pi-可补Finite Groups p-Nilpotent&Pi-Supplemented

摘要:
H是群G的子群,如果对群G的任意主因子L/K,|G/K:NG/K(HK/KIL/K)|是 π(HK/KIL/K)-数,则称H在G中满足π-性质;如果存在G的子群T使得G=HT,并且HIT≤I≤H,其中I在G中满足π-性质,则称H在G中是π-可补充的。利用子群的π-可补充性,得到了有限群p-幂零性的一个新的判定方法。

Abstract: Let H be a subgroup G . If every chief factor L/K of G, |G/K:NG/K(HK/KIL/K)| is a π(HK/KIL/K)-number, then H is called satisfying π-property in G. If there exists a subgroup  T of  G such that  G=HT and HIT≤I≤H , where I satisfies π-property in G , then H is called  π-supplemented in G . By the property of  π-supplemented, some new criterion of p-nilpotency of finite groups is obtained.

文章引用: 李保军 , 刘阿明 (2014) Π-可补充子群对有限群结构的影响。 理论数学, 4, 167-171. doi: 10.12677/PM.2014.45025

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