Groupes dont les sous-groupes de rang infini ont des layers de Chernikov ou polycycliques-par-finis

Abstract

Otal and Peña have characterized minimal non-( FA)-groups and groups that have few non-( FA)-subgroups in the class of locally graded groups. In this thesis we generalize these results to the class PFA. In 1988 J. Otal and J. M. Peña studied minimal non- -groups, they have shown that any minimal non- -group is perfect and F-perfect. We also generalize this result to minimal non- -groups. In 2017, M. Bouchelaghem and N. Trabelsi have shown that if is a locally (soluble-by-finite) group of infinite rank and without simple homomorphic images of infinite rank with each proper subgroup of infinite rank is X -group, then so are all proper subgroups of , where X is a class of soluble-by-finite minimax groups. We have established a similar result for the class of X XA-groups, where X is either the class of polycyclic-by-finite or Chernikov groups.