Abstract
A subgroup of a group is called almost normal if it has only finitely many conjugates, or equivalently if its normalizer has finite index in the group. A famous theorem by B.H. Neumann states that all subgroups of a group G are almost normal if and only if the centre Z(G) has finite index in G. Here the structure of groups in which every subgroup is pronormal in a subgroup of finite index is investigated.
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