Year: 2025
Type: 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.
Authors: Jones, Gareth A., Mačaj, Martin
Institutions: University of Southampton, Comenius University Bratislava
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2846944527, Výnimočné štruktúry v diskrétnej matematike, G3878479425, Výnimočné štruktúry v diskrétnej matematike: vlastnosti, konštrukcie a klasifikácie, G5068321180, G5243991293, Teória grafov v kontexte modernej matematiky, Kombinatorické štruktúry s predpísanými symetriami, G6873202014, G8088548421
OpenAlex ID: W7126337884
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