On groups in which subnormal subgroups of infinite rank are commensurable with some normal subgroup
Group Theory
2021-03-18 v1
Abstract
We study soluble groups G in which each subnormal subgroup H with infinite rank is commensurable with a normal subgroup, i.e. there exists a normal subgroup N such that the intersection of H and N has finite index in both H and N. We show that if such a G is periodic, then all subnormal subgroups are commensurable with a normal subgroup, provided either the Hirsch-Plotkin radical of G has infinite rank or G is nilpotent-by-abelian (and has infinite rank).
Keywords
Cite
@article{arxiv.2103.09719,
title = {On groups in which subnormal subgroups of infinite rank are commensurable with some normal subgroup},
author = {Ulderico Dardano and Fausto De Mari},
journal= {arXiv preprint arXiv:2103.09719},
year = {2021}
}