On Normal Subgroups of Products of Nilpotent Groups

Abstract

Let G be a group factorized by finitely many pairwise permutable nilpotent subgroups. The aim of this paper is to find conditions under which at least one of the factors is contained in a proper normal subgroup of G.

Some Solubility Criteria in Factorised Groups

“…It is quite clear that not many properties carry over from A and B to G, and so a natural problem is: suppose that A and B belong to a certain class of groups, what can be said about G? This question has been extensively studied, with many results available spread over many papers (see [1,3]). The fact that the product of two supersoluble groups is not supersoluble in general, even when both factors are normal, has opened the door to the study of groups which are factorised as a product of two subgroups connected by some permutability properties.…”