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Classification of regular maps of prime characteristic revisited: Avoiding the Gorenstein-Walter theorem

Conder, Marston D. E. and Širáň, Jozef (2020). Classification of regular maps of prime characteristic revisited: Avoiding the Gorenstein-Walter theorem. Journal of Algebra, 548 pp. 120–133.

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DOI (Digital Object Identifier) Link: https://doi.org/10.1016/j.jalgebra.2019.12.008
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Abstract

Breda, Nedela and Širáň (2005) classified the regular maps on surfaces of Euler characteristic $-p$ for every prime $p$. This classification relies on three key theorems, each proved using the highly non-trivial characterisation of finite groups with dihedral Sylow 2-subgroups, due to D. Gorenstein and J.H. Walter (1965). Here we give new proofs of those three facts (and hence the entire classification) using somewhat more elementary group theory, using without referring to the Gorenstein-Walter theorem.

Item Type: Journal Item
ISSN: 0021-8693
Keywords: Regular map; Automorphism group; Non-orientable surface; Euler characteristic.
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 68206
Depositing User: Jozef Širáň
Date Deposited: 21 Nov 2019 09:03
Last Modified: 26 Jun 2020 08:24
URI: http://oro.open.ac.uk/id/eprint/68206
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