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REGULAR HYPERMAPS OVER PROJECTIVE LINEAR GROUPS

Part of: Low-dimensional topology Special aspects of infinite or finite groups

Published online by Cambridge University Press:  01 October 2008

MARSTON CONDER ,
PRIMOŽ POTOČNIK  and
JOZEF ŠIRÁŇ
MARSTON CONDER*
Affiliation:
Department of Mathematics, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand (email: m.conder@auckland.ac.nz)
PRIMOŽ POTOČNIK
Affiliation:
Faculty of Mathematics and Physics, University of Ljubljana, and Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI-1000 Ljubljana, Slovenia (email: primoz.potocnik@fmf.uni-lj.si)
JOZEF ŠIRÁŇ
Affiliation:
Open University, Milton Keynes, MK7 6AA, UK, and Slovak Technical University, Radlinskeho 11, 81368, Bratislava, Slovakia (email: j.siran@open.ac.uk)
*
✉For correspondence; e-mail: m.conder@auckland.ac.nz
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Abstract

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An enumeration result for orientably regular hypermaps of a given type with automorphism groups isomorphic to PSL(2,q) or PGL(2,q) can be extracted from a 1969 paper by Sah. We extend the investigation to orientable reflexible hypermaps and to nonorientable regular hypermaps, providing many more details about the associated computations and explicit generating sets for the associated groups.

Keywords

hypermapregular hypermaptriangle groupprojective linear group

MSC classification

Secondary: 57M15: Relations with graph theory 20F05: Generators, relations, and presentations

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 85 , Issue 2 , October 2008 , pp. 155 - 175
Copyright
Copyright © 2008 Australian Mathematical Society

Footnotes

The authors gratefully acknowledge the support from the NZIMA programme on Combinatorics and Its Applications. The first and third authors wish to acknowledge the partial support from the Marsden Fund, and the third author would like to acknowledge the partial support from APVV Grants Nos. 20-000704 and 0040-06.

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