Orientable and non-orientable regular maps with given exponent group

Asciak, Kirstie; Conder, Marston D.E.; Pavlíková, Soňa and Širáň, Jozef (2023). Orientable and non-orientable regular maps with given exponent group. Journal of Algebra, 620 pp. 519–533.

DOI: https://doi.org/10.1016/j.jalgebra.2023.01.004

Abstract

With the help of the parallel product (also known as the join) of maps given by subgroups of triangle groups, and some facts about automorphisms of products of simple groups, we extend a 2016 theorem of Conder and Širáň on exponent groups of orientable maps, by proving that for every d ≥ 3 and every group U of units mod d containing −1, there exist infinitely many non-orientable regular maps of valency d with exponent group equal to U.

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