Characterisations and Galois conjugacy of generalised Paley maps

Details Characterisations and Galois conjugacy of generalised Paley maps Characterisations and Galois conjugacy of generalised Paley maps

2010-06-02

arxiv.org/abs/1006.0514v1

Mathematics

Combinatorics

Scientific paper

A generalised Paley map is a Cayley map for the additive group of a finite field F, with a subgroup S=-S of the multiplicative group as generating set, cyclically ordered by powers of a generator of S. We characterise these as the orientably regular maps with orientation-preserving automorphism group acting primitively and faithfully on the vertices; allowing a non-faithful primitive action yields certain cyclic coverings of these maps. We determine the fields of definition and the orbits of the absolute Galois group on these maps, and we show that if (q-1)/(p-1) divides |S|, where |F|=q=p^e with p prime, then these maps are the only orientably regular embeddings of their underlying graphs; in particular this applies to the Paley graphs, where |S|=(q-1)/2 is even.

Affiliated with

Also associated with

No associations

Rating

Characterisations and Galois conjugacy of generalised Paley maps does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Characterisations and Galois conjugacy of generalised Paley maps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Characterisations and Galois conjugacy of generalised Paley maps will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-513040