Anti-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>
  CC</mml:mi></mml:math>-Groups and Anti-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>PC</mml:mi></mml:math>-Groups

Russo, Francesco

doi:https://doi.org/10.1155/2007/29423

International Journal of Mathematics and Mathematical Sciences

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Research Article | Open Access

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

Anti- CC-Groups and Anti-PC-Groups

Francesco Russo¹

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

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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