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 (jPj; jHj) = 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 H \T  HsG, where HsG is generated by all s-semipermutable subgroups of G contained in H. We investigate the in uence 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.