Abstract
A subgroup H of a finite group G is said to be nearly s-embedded in G if G has an s-permutable subgroup T and an s-semipermutable subgroup HssG contained in H such that and where HsG is the intersection of all s-permutable subgroups of G containing H. In this article, we investigate the influence of some nearly s-embedded subgroups of Sylow p-subgroups on the p-nilpotency of finite groups. A number of known results are improved and extended.
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