Accessible Requires Authentication Published by De Gruyter September 1, 2012

Finite groups with NR-subgroups or their generalizations

Izabela Agata Malinowska
From the journal Journal of Group Theory

Abstract.

Yakov Berkovich investigated the following concept: a subgroup H of a finite group G is called an NR-subgroup (Normal Restriction) if, whenever , , where KG is the normal closure of K in G. In this article we characterize the class of finite solvable groups in which every subnormal subgroup is normal in terms of NR-subgroups. We also give similar characterizations of the classes of finite solvable groups in which every subnormal subgroup is permutable or s-permutable. Moreover we provide some sufficient conditions for the supersolvability and p-nilpotency of finite groups.

Received: 2012-01-16
Revised: 2012-05-11
Published Online: 2012-09-01
Published in Print: 2012-09-01

© 2012 by Walter de Gruyter Berlin Boston