On some generalizations of nearly normal subgroups - Piskun, M. M.; Semko, N. N. (Ukrains’kyi Matematychnyi Zhurnal, 2009)
A subgroup H of a group G is called almost polycyclically close to a normal group (in G) if H contains a subgroup L normal in H^G for which the quotient group H^G /L is almost polycyclic. The group G is called an anti-PC-group if each its subgroup, which is not almost polycyclic, is almost polycyclically close to normal. The structure of minimax anti-PC-groups is investigated.