Realisation of groups as automorphism groups in permutational categories

Authors

DOI:

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

Keywords:

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

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.

Published

2021-08-10

Issue

Section

Articles