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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

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Source Normalized Impact per Paper (SNIP) 2018: 0.964

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Volume 11, Issue 1


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


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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