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p-Extensions of free pro-p groups
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W. N. Herfort
Published/Copyright:
August 26, 2025
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 p" 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)).
Published Online: 2025-08-26
Published in Print: 1999-08-01
© 2025 by Walter de Gruyter Berlin/Boston
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Articles in the same Issue
- Some remarks on linear structures in right distributive domains
- Distances between Banach spaces
- p-Extensions of free pro-p groups
- On the Brill-Noether problem for vector bundles
- On 4-dimensional elation Laguerre planes admitting simple Lie groups of automorphisms
- Geometric asymptotics and the logarithmic Sobolev inequality
- Contents
- Some remarks on linear structures in right distributive domains
- Distances between Banach spaces
- p-Extensions of free pro-p groups
- On the Brill - Noether problem for vector bundles
- On 4-dimensional elation Laguerre planes admitting simple Lie groups of automorphisms
- Geometric asymptotics and the logarithmic Sobolev inequality
- Instructions to Authors
- Editors
Articles in the same Issue
- Some remarks on linear structures in right distributive domains
- Distances between Banach spaces
- p-Extensions of free pro-p groups
- On the Brill-Noether problem for vector bundles
- On 4-dimensional elation Laguerre planes admitting simple Lie groups of automorphisms
- Geometric asymptotics and the logarithmic Sobolev inequality
- Contents
- Some remarks on linear structures in right distributive domains
- Distances between Banach spaces
- p-Extensions of free pro-p groups
- On the Brill - Noether problem for vector bundles
- On 4-dimensional elation Laguerre planes admitting simple Lie groups of automorphisms
- Geometric asymptotics and the logarithmic Sobolev inequality
- Instructions to Authors
- Editors
