@article {
author = {Dardano, Ulderico and De Mari, Fausto},
title = {On groups in which subnormal subgroups of infinite rank are commensurable with some normal subgroup},
journal = {International Journal of Group Theory},
volume = {11},
number = {1},
pages = {37-42},
year = {2022},
publisher = {University of Isfahan},
issn = {2251-7650},
eissn = {2251-7669},
doi = {10.22108/ijgt.2021.127143.1671},
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 $H\cap N$ 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 = {transitivity,core-finite,normal-by-finite,close to normal},
url = {https://ijgt.ui.ac.ir/article_25599.html},
eprint = {https://ijgt.ui.ac.ir/article_25599_f96d108b8c4ff490e64b857b094cb800.pdf}
}