Une propriété qui garantit qu'un groupe résoluble de type fini est périodique-par-nilpotent

Abstract

Given a class of groups we denote by the class of groups G such that for any element x in G there exists a normal subgroup H(x) with finite index in G satisfying 〈x, xh⟩ for any h  H(x). In 2024, N. Trabelsi and F. Gherbi in their article, characterized the class of groups where is either the class of finite-by-nilpotent groups (denoted ), or the class of periodic-by-nilpotent groups (denoted ). Our objective in this memorandum, is to present, with their proofs, the results obtained by N. Trabelsi and F. Gherbi in their article, concerning the two classes of groups and