Groups Whose Finitely Generated Subgroups Are Either Permutable or Pronormal

Abstract

In the current article we consider locally finite groups whose finitely generated subgroups are either permutable or pronormal.

On non-periodic groups whose finitely generated subgroups are either permutable or pronormal

“…In the paper [12], the study of groups whose finitely generated subgroups are either permutable or pronormal was initiated. More concretely, the authors described the locally finite groups whose finitely generated subgroups are either permutable or pronormal.…”

“…Olshanskij [18,Theorem 28.2] constructed an example of an infinite p-group G, where p is a big enough prime, whose proper subgroups have order p. Clearly, every subgroup of G is pronormal. The current article is a continuation of [12]. Here we consider some infinite groups whose finitely generated subgroups are either permutable or pronormal.…”