Realisation of groups as automorphism groups in permutational categories - Jones, Gareth A. (Ars mathematica contemporanea, 2021)
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: automorphism group; centraliser; centralizator; dessin d'enfant; grupa avtomorfizmov; hiperzemljevid; hypermap; map; otroška risba; permutacijska grupa; permutation group; zemljevid