On the structure of some contranormal-free groups

TL;DR

This paper investigates contranormal-free groups, proving that certain locally generalized radical contranormal-free groups with finite section rank are hypercentral, thus advancing understanding of their structure.

Contribution

It introduces the concept of contranormal-free groups and establishes new structural results, including conditions under which such groups are hypercentral.

Findings

Locally generalized radical contranormal-free groups with finite section rank are hypercentral.

Provides various results characterizing contranormal-free groups.

Advances the structural theory of contranormal-free groups.

Abstract

A subgroup of a group is contranormal if its normal closure coincides with the group. We call such groups without proper contranormal subgroups contranormal-free. In this paper we prove various results concerning contranormal-free groups proving, for example that locally generalized radical contranormal-free groups which have finite section rank are hypercentral.