论文标题
每个最大亚组都是nilpotent或正常或具有$ p'$ - 订单的有限组
Finite groups in which every maximal subgroup is nilpotent or normal or has $p'$-order
论文作者
论文摘要
令$ g $为有限的组，$ p $ $ | g | $的固定prime除数。将nilpotence，正态性和群体的顺序结合在一起，我们证明，如果每个最大亚组为$ g $是nilpotent或normal的，或者有$ p'$ - 订单，则（1）$ g $是可溶解的； （2）$ g $有一个Sylow塔； （3）最多存在一个prime除数$ q $ $ | g | $，因此$ g $既不是$ q $ nilpotent也不是$ q $，其中$ q \ q \ neq p $。
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 $q\neq p$.
