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We study groups in which each subnormal subgroup is commensurable with a normal subgroup. Recall that two subgroups  and  are termed  commensurable  ifH  ∩  KH\cap K    has finite index in both  and . Among other results, we show that if a (sub)soluble group  has the above property, then  is finite-by-metabelian, i.e.,G  ′′G^{\prime\prime}    is finite.

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