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 permuteswith 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 partiallys-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 thein uence of some partially s-embedded minimal subgroups on the nilpotency and supersolubility of afinite group g. a series of known results in the literature are unified and generalized.