Realisation of groups as automorphism groups in permutational categories
Ars mathematica contemporanea, Volume 21 (2021) no. 1, article no. 01, 22 p.
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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
Gareth A. Jones. Realisation of groups as automorphism groups in permutational categories. Ars mathematica contemporanea, Volume 21 (2021) no. 1, article no. 01, 22 p.. doi: 10.26493/1855-3974.1840.6e0
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author = {Gareth A. Jones},
title = {
{Realisation} of groups as automorphism groups in permutational categories
},
journal = {Ars mathematica contemporanea},
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year = {2021},
volume = {21},
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doi = {10.26493/1855-3974.1840.6e0},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1840.6e0/}
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