The regular objects in various categories, such as maps, hypermaps or covering spaces, can be identified with the normal subgroups N of a given group Γ , with automorphism group isomorphic to Γ / N. It is shown how to enumerate such objects with a given finite automorphism group G, how to represent them all as quotients of a single regular object U(G), and how the outer automorphism group of Γ acts on them. Examples constructed include kaleidoscopic maps with trinity symmetry.
@article{545,
title = {Combinatorial categories and permutation groups},
journal = {ARS MATHEMATICA CONTEMPORANEA},
volume = {11},
year = {2015},
doi = {10.26493/1855-3974.545.fd5},
language = {EN},
url = {http://dml.mathdoc.fr/item/545}
}
Jones, Gareth. Combinatorial categories and permutation groups. ARS MATHEMATICA CONTEMPORANEA, Tome 11 (2015) . doi : 10.26493/1855-3974.545.fd5. http://gdmltest.u-ga.fr/item/545/