FINITE GROUPS WITH s-ABNORMAL SCHMIDT SUBGROUPS

Let G be a finite group and lets = {s(i)| i? I} be a partition of the set of all primes P. The group G is s-primary if G is a si-group for some i ? I; while G is s-nilpotent if G is the direct product of s-primary subgroups; and G is a Schmidt group if G is nonnilpotent but each proper subgroup in G is nilpotent. A subgroup A of G is s-abnormal in G if for all subgroups K < H in G, where A < K, the quotient group H/K-H is not a-primary. We describe the structure of finite groups whose every non -a-nilpotent Schmidt subgroup is a-abnormal.