Document Type : Research Paper
Chongqing University of Arts and Sciences, P R China
Chongqing University of Arts and Sciences
Let H be a subgroup of a group G. H is said to be S-embedded in G if G has a normal
T such that HT is an S-permutable subgroup of G and H ∩ T ≤ H
sG, where H denotes the subgroup generated by all those subgroups of H which are S-permutable in G. In this paper, we investigate the inﬂuence of minimal S-embedded subgroups on the structure of ﬁnite groups.
We determine the structure the ﬁnite groups with some minimal S-embedded subgroups. We also give
some new characterizations of p-nilpotency of ﬁnite groups in terms of S-embedding property. As applications, some previous known results are generalized.