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arXiv · 2010.04808

Finite groups whose maximal subgroups of order divisible by all the primes are supersolvable

Alexander Moretó
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Abstract

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.

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Alexander Moretó. 2020-10-09. Finite groups whose maximal subgroups of order divisible by all the primes are supersolvable. https://arxiv.org/abs/2010.04808

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