Realisation of groups as automorphism groups in permutational categories
Realisation of groups as automorphism groups in permutational categories
It is shown that in various categories, including many consisting of maps or hypermaps, oriented or unoriented, of a given hyperbolic type, or of coverings of a suitable topological space, every countable group A is isomorphic to the automorphism group of uncountably many non-isomorphic objects, infinitely many of them finite if A is finite. In particular, the latter applies to dessins d’enfants, regarded as finite oriented hypermaps.
Automorphism group, Centraliser, Dessin d’enfant, Hypermap, Map, Permutation group
Jones, Gareth A.
fdb7f584-21c5-4fe4-9e57-b58c78ebe3f5
10 August 2021
Jones, Gareth A.
fdb7f584-21c5-4fe4-9e57-b58c78ebe3f5
Jones, Gareth A.
(2021)
Realisation of groups as automorphism groups in permutational categories.
Ars Mathematica Contemporanea, 21 (1).
(doi:10.26493/1855-3974.1840.6e0).
Abstract
It is shown that in various categories, including many consisting of maps or hypermaps, oriented or unoriented, of a given hyperbolic type, or of coverings of a suitable topological space, every countable group A is isomorphic to the automorphism group of uncountably many non-isomorphic objects, infinitely many of them finite if A is finite. In particular, the latter applies to dessins d’enfants, regarded as finite oriented hypermaps.
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Accepted/In Press date: 18 July 2020
Published date: 10 August 2021
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© 2021 Society of Mathematicians, Physicists and Astronomers of Slovenia. All rights reserved.
Keywords:
Automorphism group, Centraliser, Dessin d’enfant, Hypermap, Map, Permutation group
Identifiers
Local EPrints ID: 475537
URI: http://eprints.soton.ac.uk/id/eprint/475537
ISSN: 1855-3966
PURE UUID: 150b2b32-d706-4579-abcc-874437343ad3
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Date deposited: 21 Mar 2023 17:41
Last modified: 17 Mar 2024 01:05
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Author:
Gareth A. Jones
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