Product of min-by-max subgroups and relations with residual finite group

A group G is called min-by-max if it has a normal subgroup N with minimal condition such that the factor group G/N satisfies the maximal condition. And the finite residual J(G) of a group G isthe intersection of all normal subgroups of finite index of G. In this paper we show that if A1,A2,…,An are finitely many pairwise permutable abelian min-by-max subgroups of the group G such that G=A1…An, then G is a soluble min-by-max group and J(G)=J(A1)…J(An).

Keywords:

min-by-max , minimal condition , maximal condition , finite residual group