%0 Journal Article
%T On groups in which subnormal subgroups of infinite rank are commensurable with some normal subgroup
%J International Journal of Group Theory
%I University of Isfahan
%Z 2251-7650
%A Dardano, Ulderico
%A De Mari, Fausto
%D 2022
%\ 03/01/2022
%V 11
%N 1
%P 37-42
%! On groups in which subnormal subgroups of infinite rank are commensurable with some normal subgroup
%K transitivity
%K core-finite
%K normal-by-finite
%K close to normal
%R 10.22108/ijgt.2021.127143.1671
%X 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).
%U https://ijgt.ui.ac.ir/article_25599_f96d108b8c4ff490e64b857b094cb800.pdf