Quotient groups of locally graded groups and groups of certain Kurosh-Chernikov classes

Abstract

We establish the validity of the inclusion G/N∈ X for groups G ∈ X under certain restrictions on N ⊴ G, where X is one of the following classes, the class of locally graded groups, the class of RI-groups, or the class $\hat P\mathfrak{Y}$ for a fixed group variety $\mathfrak{Y} \supseteq \mathfrak{A}$