On groups which are the product of abelian subgroups

Abstract

If the group G = AB is the product of two abelian subgroups A and B, then G is metabelian by a well-known result of Ito [8], so that the commutator subgroup G' of G is abelian. In the following we are concerned with the following condition:There exists a normal subgroup N^

On Normal Subgroups of Products of Nilpotent Groups

“…Finally we note that the dual problem of the existence of a non-trivial normal subgroup of the factorized group G = AB ¥= 1 contained in A or B has been studied for instance in [19] and [4]; Zaidev shows for example that this condition holds if A and B are abelian and one of them has finite sectional rank. The example of Howlett in [9] mentioned above also shows that this cannot be extended to the case when A and B are abelian with finite torsion-free rank, and it also becomes false for finite products of two nilpotent groups (see [2] or [8]).…”

Product of Polycyclic-by-Finite Groups (PPFG)

“…This combines theorems of B. Amberg (see [1][2][3][4] and [6]) , N.S. Chernikov (see [5]), S. Franciosi, F. de Giovanni (see [3,6,[32][33][34][35][36]), O.H.Kegel (see [8]), J.C.Lennox (see [12]) , D.J.S. Robinson(see [9] and [15]), J.E.…”