On Groups Whose Proper Subgroups Are Chernikov-by-Baer or (Periodic Divisible Abelian)-by-Baer

Abstract

Communicated by A. FacchiniIf X is a class of groups, then a group G is called a minimal non-X-group if it is not an X-group but all of its proper subgroups belong to X. In this paper we prove that locally graded minimal non-(Chernikov-by-nilpotent)-groups are precisely minimal non-nilpotent-groups without maximal subgroups and that locally graded minimal non-(Chernikov-by-Baer)-groups are locally finite and coincide with the normal closure of an element. We also prove that an infinite locally graded minimal non-((periodic divisible abelian)-by-Baer)-group G is an imperfect locally nilpotent p-group, for some prime p, and there is an element a in G such that G = a G .