On the structure of some locally nilpotent groups without contranormal subgroups
Group Theory
2020-06-04 v1
Abstract
Following J.S. Rose, a subgroup H of a group G is said contranormal in G if G = H^G . In a certain sense, contranormal subgroups are antipodes to subnormal subgroups. It is well known that a finite group is nilpotent if and only if it has no proper contranormal subgroups. We prove that a nilpotent-by-finite group with no proper contranormal subgroup is nilpotent. There are locally nilpotent groups with a proper contranormal subgroup. We study the structure of hypercentral groups with a finite proper contranormal subgroup.
Keywords
Cite
@article{arxiv.2006.02345,
title = {On the structure of some locally nilpotent groups without contranormal subgroups},
author = {Leonid A. Kurdachenko and Patrizia Longobardi and Mercede MAJ},
journal= {arXiv preprint arXiv:2006.02345},
year = {2020}
}