Some Finite Nonsolvable Groups Characterized by Their Solvable Subgroups

<正> Let G be a finite nonsolvable group and H a proper subgroup of G.In this paper wedetermine the structure of G if G satisfies one of the following conditions:(1)Every solvable subgroup K(KH)is eitherp-decomposable or a Schmidt group,p being thesmallest odd prime factor of |G|.(2)|G:H| is divisible by an odd prime and every solvable subgroup K(KH)is either 2'-closed ora Schmidt group.(3)|G:H|is even and every solvable subgroup K(KH)is either 2-closed or a Schmidt group.