Gruppi fattorizzati da sottogruppi abeliani

Abstract

Let G = _A_1_A_2_A_3 be a group that is a product of three mutually permutable abelian subgroups _A_1, _A_2 and _A_3. In this paper we prove that if _A_1_A_2 is nilpotent then G is soluble and that if _A_1_A_2, _A_1_A_3 and _A_2_A_3 are nilpotent then G is also nilpotent.