Groupes dont les sous-groupes propres sont fini-par-hypercentraux

Abstract

The aim of this thesis concerns the study of minimal non-Ω groups, where Ω is a given class of groups, i.e. the study of groups not belonging to Ω but all of proper subgroups are in Ω. Many results on infinite minimal non-Ω groups, for various classes of Ω groups, have been obtained by different authors. In this thesis, we propose to describe the minimal non-(finite-by-hypercentral) groups. The main result of this thesis asserts that the locally graded minimal non-(finite-by hypercentral) groups are exactly either locally graded minimal non-(finite-by-abelian), or locally graded minimal non-hypercentral groups.