Let d be the smallest generator number of a finite p-group P and let Md(P) = {P1,...,Pd} be a set of maximal subgroups of P such that ∩di=1 Pi = Φ(P). In this paper, we study the structure of a finite group G under the assumption that every member in Md(Gp) is S-semipermutable in G for each prime divisor p of |G| and a Sylow p-subgroup Gp of G.
For a finite group G, let S（G） be the set of minimal subgroups of odd order,which are complemented in G. It is proved that if every minimal subgroup X of odd orderof G which does not belong to S（G）, CG（X） is either subnormal or abnormal in G. Then Gsolvable.
