Realisation of groups as automorphism groups in permutational categories

Gareth A. Jones


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.


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

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ISSN: 1855-3974

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