Frobenius groups which are the automorphism groups of orientably-regular maps

Yan Wang, Hai-Peng Qu, Kai Yuan

Abstract


In this paper, we prove that a Frobenius group (except for those which are also Dihedral groups) can only be the automorphism group of an orientably-regular chiral map. The necessary conditions for a Frobenius group to be the automorphism group of an orientbly-regular chiral map are given. And in the sense of Frobenius groups, these necessary conditions are also sufficient. Moreover,  Frobenius groups fulfilling these necessary conditions are also constructed.

Keywords


Frobenius group; (orientably) regular map; automorphism group

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DOI: https://doi.org/10.26493/1855-3974.1851.b44

ISSN: 1855-3974

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