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We study soluble groups G in which each subnormal subgroup H with infiniterank is commensurable with a normal subgroup, i.e. there exists a normalsubgroup N such that the intersection of H and N has finite index in both H andN. We show that if such a G is periodic, then all subnormal subgroups arecommensurable with a normal subgroup, provided either the Hirsch-Plotkinradical of G has infinite rank or G is nilpotent-by-abelian (and has infiniterank).

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