Frobenius群是可定向正则映射的自同构群

Ars Math. Contemp. Pub Date : 2020-11-22 DOI:10.26493/1855-3974.1851.b44

H. Qu, Yan Wang, Kai Yuan

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摘要

本文证明了一个Frobenius群(二面体群除外)只能是一个可定向正则手性映射的自同构群。给出了Frobenius群是可定向正则手性映射的自同构群的充分必要条件。进一步证明了这些具有Frobenius自同构的可定向正则手性映射是正规的Cayley映射。也构造了符合这些条件的Frobenius群。

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

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.

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Ars Math. Contemp.

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