International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 29423, 11 pages
doi:10.1155/2007/29423
Research Article
Anti-
CC-Groups and Anti-PC-Groups
Department of Mathematics, Faculty of Mathematics, University of Naples, Via Cinthia, Naples 80126, Italy
Received 8 October 2007; Accepted 15 November 2007
Academic Editor: Alexander Rosa
Copyright © 2007 Francesco Russo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.