Conder, Marston; Potočnik, Primož and Širáň, Jozef
(2010).
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| DOI (Digital Object Identifier) Link: | http://dx.doi.org/doi:10.1016/j.jalgebra.2010.07.047 |
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| Google Scholar: | Look up in Google Scholar |
Abstract
A regular map M is a cellular decomposition of a surface such that its automorphism group Aut(M) acts transitively on the flags of M. It can be shown that if a Sylow subgroup P≤Aut(M) has order coprime to the Euler characteristic of the supporting surface, then P is cyclic or dihedral. This observation motivates the topic of the current paper, where we study regular maps whose automorphism groups have the property that all their Sylow subgroups contain a cyclic subgroup of index at most 2. The main result of the paper is a complete classification of such maps. As an application, we show that no regular maps of Euler characteristic −p2 exist for p a prime greater than 7.
| Item Type: | Journal Article |
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| Copyright Holders: | 2010 Elsevier Inc. |
| ISSN: | 0021-8693 |
| Keywords: | regular maps; graph embeddings; arc-transitive graphs |
| Academic Unit/Department: | Mathematics, Computing and Technology > Mathematics and Statistics |
| Item ID: | 30412 |
| Depositing User: | Jozef Siran |
| Date Deposited: | 08 Dec 2011 16:38 |
| Last Modified: | 03 Dec 2012 15:34 |
| URI: | http://oro.open.ac.uk/id/eprint/30412 |
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