Abstract
We discuss whether finiteness properties of a profinite group G can be deduced from the probabilistic zeta function P G(s). In particular we prove that in the prosoluble case, if P G(s) is rational then G/Frat(G) is finite.
Editor-in-Chief: Wilson, John S.
Managing Editor: Howie, James / Kramer, Linus / Parker, Christopher W.
Editorial Board Member: Abért, Miklós / Borovik, Alexandre V. / Boston, Nigel / Bridson, Martin R. / Caprace, Pierre-Emmanuel / Giovanni, Francesco / Guralnick, Robert / Jaikin Zapirain, Andrei / Kessar, Radha / Khukhro, Evgenii I. / Kochloukova, Dessislava H. / Malle, Gunter / Olshanskii, Alexander / Remy, Bertrand / Robinson, Derek J.S. / Willis, George
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Profinite groups with a rational probabilistic zeta function
Citation Information: Journal of Group Theory. Volume 9, Issue 2, Pages 203–217, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: 10.1515/JGT.2006.014, May 2006
Publication History:
- Received:
- 2005-02-04
- Published Online:
- 2006-05-16
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