Abnormal and pronormal subgroups have appeared in the process of investigation of some important subgroups of finite (soluble) groups such as Sylow subgroups, Hall subgroups, system normalizers, and Carter subgroups. Let H be a subgroup of a group G. We recall that a subgroup H is abnormal in G if g ∈ 〈H, Hg〉 for each element g ∈ G; and a subgroup H is pronormal in G if for each element g ∈ G, H and Hg are conjugate in 〈H, Hg〉. Pronormal subgroups have been introduced by P. Hall in his lectures in Cambridge; he also introduced abnormal subgroups in his paper, whereas the term abnormal comes from R. Carter. These subgroups and their generalizations have shown to be very useful in the finite group theory. It appears to be logical to employ such fruitful concepts in infinite groups. However, in some classes of infinite groups these mentioned subgroups gain such properties that they cannot posses in the finite case. For example, it is well-known that every finite p-group has no proper abnormal subgroups. Nevertheless, A. Yu. Olshanskii has constructed a series of impressive examples of infinite finitely generated p-groups saturated with abnormal subgroups. Concretely, for a large enough prime p there exists an infinite p-group G whose all proper subgroups have prime order p [18, Theorem 28.1]. In particular, every proper non-identity subgroup of G is maximal, and being non-normal, is abnormal.