Про групи з умовою щільності нормальності для неперіодичних неабелевих підгруп

Abstract

We will say that a non-Abelian group G has a dense system of normal non-periodic non-Abelian subgroups, if for any such pair of non-periodic non-Abelian subgroups A <B that A is not maximal in B, there is a normal subgroup N located between A and B, ie. A ≤ N ≤ B (CDN[NN]-group). In this paper, it is proved that the locally graded CDN[NN]-group with Abelian periodic commutant is metamamiltonian.