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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Neeb, Karl-Hermann / Noguchi, Junjiro / Shahidi, Freydoon / Sogge, Christopher D. / Wienhard, Anna

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Volume 11, Issue 1

Issues

p-Extensions of free pro-p groups

W.N Herfort / L Ribes / P.A Zalesskii
Published Online: 2008-03-11 | DOI: https://doi.org/10.1515/form.11.1.49

Abstract

It is proved that a virtually free pro-p group G having a free pro-p subgroup of index p satisfies a pro-p version of the Dyer-Scott structure theorem (Comm. Alg. 3(3) (1975), 195–201). The pro-2 case had been settled by W. Herfort and P. Zalesskii in (manuscr. math. 93, 457–464 (1997)). A proof for (topologically) finitely generated G has been given by C. Scheiderer.

A consequence of our result is that for any automorphism of order pn of a free pro-p group its fixed point group is a free factor.

The main theorem generalizes Serre's well known result, stating that any virtually free torsion free pro-p group is free pro-p (Topology 3, 413–420, (1965)).

About the article


Received: 1997-04-03

Revised: 1997-10-08

Published Online: 2008-03-11

Published in Print: 1999-02-15


Citation Information: Forum Mathematicum, Volume 11, Issue 1, Pages 49–61, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/form.11.1.49.

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[1]
Dessislava H. Kochloukova and Pavel A. Zalesskii
The Quarterly Journal of Mathematics, 2007, Volume 58, Number 1, Page 47
[3]
John Jossey
Journal of Number Theory, 2007, Volume 124, Number 1, Page 42
[4]
W. Herfort and P.A. Zalesskii
Journal of Algebra, 1999, Volume 216, Number 2, Page 511

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