Combinatorial categories and permutation groups

Gareth A. Jones


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.


Regular map, regular hypermap, covering space, permutation group, category

Full Text:



ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications