Groups in which each subgroup is commensurable with a normal subgroup
Group Theory
2017-05-09 v1
Abstract
A group G is a cn-group if for each subgroup H of G there exists a normal subgroup N of G such that the index of both H and N in HN is finite. The class of cn-groups contains properly the classes of core- finite groups and that of groups in which each subgroup has finite index in a normal subgroup. In the present paper it is shown that a cn-group whose periodic images are locally finite is finite-by-abelian-by-finite. Such groups are then described into some details by considering automorphisms of abelian groups. Finally, it is shown that if G is a locally graded group with the property that the above index is bounded independently of H, then G is finite-by-abelian-by-finite.
Cite
@article{arxiv.1705.02360,
title = {Groups in which each subgroup is commensurable with a normal subgroup},
author = {Carlo Casolo and Ulderico Dardano and Silvana Rinauro},
journal= {arXiv preprint arXiv:1705.02360},
year = {2017}
}