Self-dual, self-Petrie-dual and Möbius regular maps on linear fractional groups

Erskine, Grahame; Hriňáková, Katarína and Reade Jeans, Olivia (2020). Self-dual, self-Petrie-dual and Möbius regular maps on linear fractional groups. The Art of Discrete and Applied Mathematics, 3(1), article no. 3.

DOI: https://doi.org/10.26493/2590-9770.1263.86e

Abstract

Regular maps on linear fractional groups PSL(2, q) and PGL(2, q) have been studied for many years and the theory is well-developed, including generating sets for the associated groups. This paper studies the properties of self-duality, self-Petrie-duality and Möbius regularity in this context, providing necessary and sufficient conditions for each case. We also address the special case for regular maps of type (5, 5). The final section includes an enumeration of the PSL(2, q) maps for q ≤ 81 and a list of all the PSL(2, q) maps which have any of these special properties for q ≤ 49.

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About

• Item ORO ID
• 72269
• Item Type
• Journal Item
• ISSN
• 2590-9770
• Extra Information
• Article is a part of the Special issue of ADAM devoted to the International Workshop on Symmetries of Graph and Networks 2018
• Keywords
• Regular map; external symmetry; self-dual; self-Petrie-dual; Mobius regular
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM)
  Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
• Related URLs
• • http://export.arxiv.org/abs/1807.11307(Other)
• Depositing User
• Olivia Reade