International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2007 / Article

Research Article | Open Access

Volume 2007 |Article ID 029423 | https://doi.org/10.1155/2007/29423

Francesco Russo, "Anti- CC-Groups and Anti-PC-Groups", International Journal of Mathematics and Mathematical Sciences, vol. 2007, Article ID 029423, 11 pages, 2007. https://doi.org/10.1155/2007/29423

Anti- CC-Groups and Anti-PC-Groups

Academic Editor: Alexander Rosa
Received08 Oct 2007
Accepted15 Nov 2007
Published20 Jan 2008

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.

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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.


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