A subgroup H of a group G is said to be abnormal in G if g ∈ <H, Hg> for each element g ∈ G. It is well known that every locally nilpotent group has no proper abnormal subgroups, but it is an open question whether the converse holds. In this article we prove this conjecture for some classes of infinite groups. In particular, it is proved that an FC-nilpotent group without proper abnormal subgroups is hypercentral. Also groups with finitely many abnormal subgroups are considered.
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