On groups in which subnormal subgroups of infinite rank are commensurable‎ ‎with some normal subgroup

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)‎.

Abstract licence: CC BY

11 more references, whose wording the paper’s licence keeps private.

A person counts once a day per paper. We keep no cookie and no address: a reader is a hash that changes every day. Any month under five reads shows no number.