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Fixed Points of Automorphisms of Free Pro-p Groups of Rank 2

Published online by Cambridge University Press:  20 November 2018

Wolfgang N. Herfort ,
Luis Ribes  and
Pavel A. Zalesskii
Wolfgang N. Herfort
Affiliation:
Institute fi Angew. und Numer. Mathematik Technische Universität Wien A-1040 Wien Austria e–mail: herfort@uranus.tuwien.ac.at
Luis Ribes
Affiliation:
Institute fi Angew. und Numer. Mathematik Technische Universität Wien A-1040 Wien Austria e–mail: herfort@uranus.tuwien.ac.at
Pavel A. Zalesskii
Affiliation:
Institute of Techn. Cybernetics Academy of Sciences 220605 Minsk Byelorussia e–mail: mahaniok%bas10.basnet.minsk.by@demos.su
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Abstract

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Let p be a prime number, and let F be a free pro-p group of rank two. Consider an automorphism α of F of finite order m, and let FixF(α) = {x ∈ F | α(x) = x} be the subgroup of F consisting of the elements fixed by α. It is known that if m is prime to p and α = idF, then the rank of FixF(α) is infinite. In this paper we show that if m is a finite power pr of p, the rank of FixF(α) is at most 2. We conjecture that if the rank of F is n and the order of a is a power of α, then rank (FixF(α)) ≤ n.

Keywords

20E1820E3622C05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 2 , 01 April 1995 , pp. 383 - 404
Copyright
Copyright © Canadian Mathematical Society 1995

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