On Minimal Non-(residually Nilpotent) Locally Graded Groups

Abstract

In this work, characterizations of a locally graded periodic group whose proper subgroups are residually nilpotent are obtained. It is shown that if such a group is minimal non-(residually nilpotent), then, under certain conditions, it has a homomorphic image which is a barely transitive group. In particular a minimal non-hypercentral group whose proper subgroups are residually nilpotent has a barely transitive homomorphic image. As an application a related question about Heineken-Mohamed-type groups is answered. Finally, a short proof and a generalization of a result on the solvability of locally graded groups is given.