论文标题
有限组的最大订单亚组可除以所有素数
Finite groups whose maximal subgroups of order divisible by all the primes are supersolvable
论文作者
论文摘要
我们将有限的组$ g $与该物业一起研究，该物业对于$ g $中的任何子组$ m $ M $ Maxal，其订单可除以$ | g | $，$ m $的所有主要除数，$ m $都是可验证的。我们表明，任何非亚伯语简单组都可以作为此类组的组成因素出现，并且如果$ g $是可解决的，那么niltotency的长度和等级是任意的。另一方面，对于每个Prime $ P $，此类组的$ P $长度最多为$ 1 $。这回答了V. Monakhov在Kourovka笔记本上提出的问题。
We study finite groups $G$ with the property that for any subgroup $M$ maximal in $G$ whose order is divisible by all the prime divisors of $|G|$, $M$ is supersolvable. We show that any nonabelian simple group can occur as a composition factor of such a group and that, if $G$ is solvable, then the nilpotency length and the rank are arbitrarily large. On the other hand, for every prime $p$, the $p$-length of such a group is at most $1$. This answers questions proposed by V. Monakhov in The Kourovka Notebook.
