Anti- CC-Groups and Anti-PC-Groups

A group G has Černikov classes of conjugate subgroups if the quotient group G/ coreG(NG(H)) is a Černikov group for each subgroup H of G. An anti-CC-group G is a group in which each nonfinitely generated subgroup K has the quotient group G/ coreG(NG(K)) which is a Černikov group. Analogously, a groupG has polycyclic-by-finite classes of conjugate subgroups if the quotient group G/coreG(NG(H)) is a polycyclic -byfinite group for each subgroup H of G. An anti-PC-group G is a group in which each nonfinitely generated subgroup K has the quotient group G/coreG(NG(K)) which is a polycyclic-by-finite group. Anti-CC-groups and anti-PC-groups are the subject of the present article.