International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 29423, 11 pages
doi:10.1155/2007/29423

Anti- CC-Groups and Anti-PC-Groups

Abstract

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 group G has polycyclic-by-finite classes of conjugate subgroups if the quotient group G/coreG(NG(H)) is a polycyclic-by-finite 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.