August 1, 1999

p-Extensions of free pro-p groups

Key Points

A virtually free pro-p group with a free pro-p subgroup of index p satisfies a pro-p version of the Dyer-Scott theorem.
The result indicates the fixed point group of an automorphism of order p in a free pro-p group is a free factor.
Generalizing previous results, the study confirms that any virtually free torsion free pro-p group is also free pro-p.
The proof resonates with earlier work, enhancing our understanding of p-extensions and group structures.

Abstract

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)).

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Cite This Study

Herfort et al. (Sun,) studied this question.

synapsesocial.com/papers/68af66dfad7bf08b1eae62bd https://doi.org/https://doi.org/10.1515/forum-1999-110103

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