  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 the intersection of H and 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).
