Partially S-embedded minimal subgroups of finite groups

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|)=۱)‎, ‎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 H\cap T\leq 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.‎

کلیدواژه ها:

s-permutable subgroup ، partially S-embedded subgroup ، nilpotent group ، Formation