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

被引：0
|
作者：
Alexander Moretó
机构：
[1] Universitat de València,Departament de Matemàtiques
来源：
Monatshefte für Mathematik | 2021年 / 195卷
关键词：
Supersolvable subgroup; Maximal subgroup; Simple group; Solvable group; -Length; Fitting height; 20D10; 20F16;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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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页码：497 / 500
页数：3
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