Groups in which each subnormal subgroup is commensurable with some normal subgroup.

We study groups in which each subnormal subgroup is commensurable with a normal subgroup. Recall that two subgroups H and K are termed commensurable if H ∩ K has finite index in both H and K. Among other results, we show that if a (sub)soluble group G has the above property, then 𝐺 is finite-by-metabelian, i.e., G ′′ is finite. [ABSTRACT FROM AUTHOR]