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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