The nilpotency of some groups with all subgroups subnormal
- Smith, Howard
- Kurdachenko, Leonid A.
ISSN: 0214-1493
Year of publication: 1998
Volume: 42
Issue: 2
Pages: 411-421
Type: Article
More publications in: Publicacions matematiques
Abstract
Let $G$ be a group with all subgroups subnormal. A normal subgroup $N$ of $G$ is said to be $G$-minimax if it has a finite $G$-invariant series whose factors are abelian and satisfy either $\max$-$G$ or $\min$-$G$. It is proved that if the normal closure of every element of $G$ is $G$-minimax then $G$ is nilpotent and the normal closure of every element is minimax. Further results of this type are also obtained.