Conder, Marston; Potočnik, Primož and Širáň, Jozef
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|DOI (Digital Object Identifier) Link:||http://dx.doi.org/10.1016/j.jalgebra.2010.07.047|
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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|
|Copyright Holders:||2010 Elsevier Inc.|
|Keywords:||regular maps; graph embeddings; arc-transitive graphs|
|Academic Unit/Department:||Mathematics, Computing and Technology > Mathematics and Statistics|
|Depositing User:||Jozef Širáň|
|Date Deposited:||08 Dec 2011 16:38|
|Last Modified:||03 Dec 2012 15:34|
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