1.
Regular maps with primitive automorphism groupsGareth A. Jones,
Martin Mačaj, 2025, original scientific article
Abstract: We classify the regular maps ℳ which have automorphism groups G acting faithfully and primitively on their vertices. As a permutation group G must be of almost simple or affine type, with dihedral point stabilisers. We show that all such almost simple groups, namely all but a few groups PSL2(q), PGL2(q) and Sz(q), arise from regular maps, which are always non-orientable. In the affine case, the maps ℳ occur in orientable and non-orientable Petrie dual pairs. We give the number of maps associated with each group, together with their genus and extended type. Some of this builds on earlier work of the first author on generalised Paley maps, and on recent work of Jajcay, Li, Širáň and Wang on maps with quasiprimitive automorphism groups.
Keywords: regular map, automorphism group, primitive, almost simple, affine group
Published in RUP: 04.11.2025; Views: 400; Downloads: 2
Full text (512,34 KB)
