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On endomorphisms of the direct product of two free groups

  • André Carvalho EMAIL logo
Published/Copyright: November 15, 2022

Abstract

We describe the endomorphisms of the direct product of two free groups of finite rank and obtain conditions for which the subgroup of fixed points is finitely generated, and we do the same for periodic points. We also describe the automorphisms of such a group and solve the three Whitehead problems for automorphisms, monomorphisms and endomorphisms for groups in this class. We also obtain conditions for an endomorphism to be uniformly continuous when a suitable metric is considered and study infinite fixed points of the extension to the completion of the group.

Award Identifier / Grant number: SFRH/BD/145313/2019

Funding statement: The author was supported by the grant SFRH/BD/145313/2019 funded by Fundação para a Ciência e a Tecnologia (FCT).

Acknowledgements

The author is grateful to Pedro Silva for fruitful discussions of these topics and to the anonymous referee for helpful comments and suggestions that greatly improved the paper.

  1. Communicated by: Alexander Olshanskii

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Received: 2021-11-26
Revised: 2022-04-27
Published Online: 2022-11-15
Published in Print: 2023-07-01

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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