Realisation of groups as automorphism groups in permutational categories

Gareth A. Jones

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.


Keywords


Permutation group, centraliser, automorphism group, map, hypermap, dessin d'enfant

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DOI: https://doi.org/10.26493/1855-3974.1840.6e0

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications