%0 Journal Article
%T Partially S-embedded minimal subgroups of finite groups
%A Tao Zhao
%A Qingliang Zhang
%J International Journal of Group Theory
%D 2013
%I University of Isfahan
%X Suppose that H is a subgroup of G, then H is said to be s-permutable in G, if H permutes with every Sylow subgroup of G. If HP=PH hold for every Sylow subgroup P of G with (|P|, |H|)=1), then H is called an s-semipermutable subgroup of G. In this paper, we say that H is partially S-embedded in G if G has a normal subgroup T such that HT is s-permutable in G and Hcap Tleq H_{overline{s}G}, where H_{overline{s}G} is generated by all s-semipermutable subgroups of G contained in H. We investigate the influence of some partially S-embedded minimal subgroups on the nilpotency and supersolubility of a finite group G. A series of known results in the literature are unified and generalized.
%K s-permutable subgroup
%K partially S-embedded subgroup
%K nilpotent group
%K formation
%U http://www.theoryofgroups.ir/?_action=showPDF&article=2751&_ob=21631b0fa51b75065747f61c434fd5e4&fileName=full_text.pdf.