Generalized Heineken Mohamed type groups

Abstract

We prove that a torsion group G with all subgroups subnormal is a nilpotent group or G = N(A1 ×· · ·×An) is a product of a normal nilpotent subgroup N and pi -subgroups Ai , where Ai = A (i) 1 · · · A (i) mi ✁ G, A (i) j is a Heineken Mohamed type group, and p1, . . . , pn are pairwise distinct primes (n ≥ 1; i = 1, . . . , n; j = 1, . . . , mi and mi are positive integers).