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: 701; Downloads: 3
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2. Super-symmetric maps from dihedral groupsŠtefan Gyürki, Ivona Hrivová, Soňa Pavlíková, 2025, original scientific article Abstract: In 1976, S. Wilson proposed to study a family of regular self-dual and self-Petrie-dual maps arising from groups of order 8n^3 defined by a specific presentation. Later on, in 2014, D. Archdeacon, M. Conder and J. Širáň proved that these maps are super-symmetric, that is, not only exhibiting all self-dualities but also all admissible exponents. Furthermore, in 2016, G. A. Jones suggested that it should be possible to obtain the same family by the means of a parallel product of maps arising from 2-extensions of dihedral groups of order 2n. In this paper we verify this suggestion for odd values of n; for even n we show that the parallel product construction gives maps that are quotients of Wilson’s maps by a normal subgroup of order 2.
Keywords: regular map, duality, exponent, super-symmetry
Published in RUP: 21.10.2025; Views: 768; Downloads: 3
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7. Regular embeddings of cycles with multiple edges revisitedKan Hu, Roman Nedela, Martin Škoviera, Naer Wang, 2015, original scientific article Abstract: Regularne vložitve ciklov z večkratnimi povezavami se pojavljajo v literaturi že kar nekaj časa, tako v topološki teoriji grafov kot tudi izven nje. Ta članek izriše kompletno podobo teh zemljevidov na ta način, da povsem opiše, klasificira in enumerira regularne vložitve ciklov z večkratnimi povezavami tako na orientabilnih kot tudi na neorientabilnih ploskvah. Večina rezultatov je sicer znana v tej ali oni obliki, toda tu so predstavljeni iz poenotenega zornega kota, osnovanega na teoriji končnih grup. Naš pristop daje dodatno informacijo tako o zemljevidih kot o njihovih grupah avtomorfizmov, priskrbi pa tudi dodaten vpogled v njihove odnose.
Keywords: regularna vložitev, večkratna povezava, Hölderjev izrek, Möbiusov zemljevid, regular embedding, multiple edge, Hölder's Theorem, Möbius map
Published in RUP: 15.10.2015; Views: 5320; Downloads: 115
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