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Regular and orientably-regular maps with quasiprimitive automorphism groups on vertices

Jajcay, Robert; Li, Cai-Heng; Širáň, Jozef and Wang, Yan (2019). Regular and orientably-regular maps with quasiprimitive automorphism groups on vertices. Geometriae Dedicata, 203(1) pp. 389–418.

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DOI (Digital Object Identifier) Link: https://doi.org/10.1007/s10711-019-00440-6
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Abstract

Regular and orientably-regular maps are central to the part of topological graph theory concerned with highly symmetric graph embeddings. Classification of such maps often relies on factoring out a normal subgroup of automorphisms acting intransitively on the set of the vertices of the map. Maps whose automorphism groups act quasiprimitively on their vertices do not allow for such factorization. Instead, we rely on classification of quasiprimitive group actions which divides such actions into eight types, and we show that four of these types, HS, HC, SD, and CD, do not occur as the automorphism groups of regular or orientably-regular maps. We classify regular and orientably-regular maps with automorphism groups of the HA type, and construct new families of regular as well as both chiral and reflexible orientably-regular maps with automorphism groups of the TW and PA types. We provide a brief summary of the known results concerning the AS type, which has been extensively studied before.

Item Type: Journal Item
Copyright Holders: 2019 Springer Nature B.V.
ISSN: 0046-5755
Project Funding Details:
Funded Project NameProject IDFunding Body
Not SetAPVV 0136/12Not Set
Not SetAPVV-15-0220Not Set
Not SetVEGA 1/0026/16Not Set
Not SetVEGA 1/0142/17Not Set
Not SetNSFC 11371307Not Set
Keywords: Regular map; Orientably-regular map; Automorphism group; Quasiprimitive group action
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 60701
Depositing User: Jozef Širáň
Date Deposited: 30 Apr 2019 14:18
Last Modified: 12 Jun 2020 20:26
URI: http://oro.open.ac.uk/id/eprint/60701
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