Groupes avec une condition sur les parties infinies

Abstract

Let X be a class of groups and let G be a group. We say that G is an X*-group (respectively, X#- group) if, and only if, every infinite subset contains two distinct elements x,y such that x, y is an X-group (respectively, y x, x is an X-group). Lennox and Wiegold draw their attention on the N*-groups and P*-groups, where N and P denotes respectively the class of nilpotent groups and polycyclic groups. In this thesis, we characterized the X#-groups where X is the class T N  and the X#-groups where X is the class Fd and TN, where (Fd), T and N denotes respectively the class of finite depth groups, torsion groups and nilpotent groups.