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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The structure of some virtually free pro-$p$ groups
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by Claus Scheiderer PDF
Proc. Amer. Math. Soc. 127 (1999), 695-700 Request permission

Abstract:

We prove two conjectures on pro-$p$ groups made by Herfort, Ribes and Zalesskii. The first says that a finitely generated pro-$p$ group which has an open free pro-$p$ subgroup of index $p$ is a free pro-$p$ product $H_0*(S_1\times H_1)*\cdots *(S_m\times H_m)$, where the $H_i$ are free pro-$p$ of finite rank and the $S_i$ are cyclic of order $p$. The second says that if $F$ is a free pro-$p$ group of finite rank and $S$ is a finite $p$-group of automorphisms of $F$, then $\operatorname {Fix}(S)$ is a free factor of $F$. The proofs use cohomology, and in particular a “Brown theorem” for profinite groups.
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Additional Information
  • Claus Scheiderer
  • Affiliation: Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany
  • MR Author ID: 212893
  • Email: claus.scheiderer@mathematik.uni-regensburg.de
  • Received by editor(s): July 1, 1997
  • Communicated by: Ronald M. Solomon
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 695-700
  • MSC (1991): Primary 20E18; Secondary 20E34, 20E36, 20E06
  • DOI: https://doi.org/10.1090/S0002-9939-99-04765-6
  • MathSciNet review: 1487337