Hole operations on Hurwitz maps
Hole operations on Hurwitz maps
For a given group G the orientably regular maps with orientation-preserving automorphism group G are used as the vertices of a graph O(G), with undirected and directed edges showing the effect of duality and hole operations on these maps. Some examples of these graphs are given, including several for small Hurwitz groups. For some G, such as the affine groups AGL1(2e), the graph O(G) is connected, whereas for some other infinite families, such as the alternating and symmetric groups, the number of connected components is unbounded.
duality, hole operation, Hurwitz group, orientably regular, Regular map
Gévay, Gábor
5202f70e-108c-43b0-b1ab-e1ab54e93464
Jones, Gareth A.
fdb7f584-21c5-4fe4-9e57-b58c78ebe3f5
Gévay, Gábor
5202f70e-108c-43b0-b1ab-e1ab54e93464
Jones, Gareth A.
fdb7f584-21c5-4fe4-9e57-b58c78ebe3f5
Gévay, Gábor and Jones, Gareth A.
(2022)
Hole operations on Hurwitz maps.
Art of Discrete and Applied Mathematics, 5 (3), [P3.01].
(doi:10.26493/2590-9770.1531.46a).
Abstract
For a given group G the orientably regular maps with orientation-preserving automorphism group G are used as the vertices of a graph O(G), with undirected and directed edges showing the effect of duality and hole operations on these maps. Some examples of these graphs are given, including several for small Hurwitz groups. For some G, such as the affine groups AGL1(2e), the graph O(G) is connected, whereas for some other infinite families, such as the alternating and symmetric groups, the number of connected components is unbounded.
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Accepted/In Press date: 19 March 2022
e-pub ahead of print date: 27 June 2022
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Funding Information:
*The authors thank the referees for a number of valuable comments. †Corresponding author. Supported by the Hungarian National Research, Development and Innovation Office, OTKA grant No. SNN 132625. E-mail addresses: gevay@math.u-szeged.hu (Gábor Gévay), G.A.Jones@maths.soton.ac.uk (Gareth A.
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© 2022 The authors.
Keywords:
duality, hole operation, Hurwitz group, orientably regular, Regular map
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Local EPrints ID: 469029
URI: http://eprints.soton.ac.uk/id/eprint/469029
PURE UUID: 602d54c9-d534-4dae-a044-1bea964d0475
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Date deposited: 05 Sep 2022 16:55
Last modified: 17 Mar 2024 13:04
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Author:
Gábor Gévay
Author:
Gareth A. Jones
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