Finite groups in which every maximal subgroup is nilpotent or normal or has p′-order

Jiangtao Shi, Na Li, R. Shen
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引用次数: 1

Abstract

Let $G$ be a finite group and $p$ a fixed prime divisor of $|G|$. Combining the nilpotence, the normality and the order of groups together, we prove that if every maximal subgroup of $G$ is nilpotent or normal or has $p'$-order, then (1) $G$ is solvable; (2) $G$ has a Sylow tower; (3) There exists at most one prime divisor $q$ of $|G|$ such that $G$ is neither $q$-nilpotent nor $q$-closed, where $q\neq p$.
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有限群,其中每个极大子群是幂零的或正规的或具有p '阶的
设$G$是有限群,$p$是$|G|$的固定素数因子。结合群的幂零性、正规性和阶性,证明了如果G$的每一个极大子群幂零或正规或p $-阶,则(1)G$是可解的;(2) $G$有一个Sylow塔;(3) $|G|$最多存在一个素因子$q$,使得$G$既不是$q$-幂零又不是$q$-闭,其中$q\neq p$。
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