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COMPUTING CENTRALISERS IN [FINITELY GENERATED FREE]-BY-CYCLIC GROUPS

Part of: Structure and classification of infinite or finite groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  04 June 2024

ANDRÉ CARVALHO Open the ORCID record for ANDRÉ CARVALHO [Opens in a new window]
ANDRÉ CARVALHO*
Affiliation:
Center for Mathematics and Applications (NOVA Math), NOVA School of Science and Technology, NOVA University Lisbon, 2829–516 Caparica, Portugal
*
e-mail: [email protected]
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Abstract

We prove that centralisers of elements in [finitely generated free]-by-cyclic groups are computable. As a corollary, given two conjugate elements in a [finitely generated free]-by-cyclic group, the set of conjugators can be computed and the conjugacy problem with context-free constraints is decidable. We pose several problems arising naturally from this work.

Keywords

centralisersfree-by-cyclic groupsconjugacy problemautomorphisms

MSC classification

Primary: 20F10: Word problems, other decision problems, connections with logic and automata
Secondary: 20E05: Free nonabelian groups 20E22: Extensions, wreath products, and other compositions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 111 , Issue 1 , February 2025 , pp. 118 - 127
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

This work is funded by national funds through the FCT–Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 and UIDP/00297/2020 (Center for Mathematics and Applications).

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