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

Hai-Peng Qu, Yan Wang, Kai Yuan

Abstract


In this paper, we prove that a Frobenius group (except for those which are dihedral groups) can only be the automorphism group of an orientably-regular chiral map. The necessary and sufficient conditions for a Frobenius group to be the automorphism group of an orientably-regular chiral map are given. Furthermore, these orientably-regular chiral maps with Frobenius automorphisms are proved to be normal Cayley maps. Frobenius groups conforming to these 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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