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An update on Hurwitz groups

An update on Hurwitz groups Abstract A Hurwitz group is any non-trivial finite quotient of the (2, 3, 7) triangle group, that is, any non-trivial finite group generated by elements x and y satisfying x 2 = y 3 = ( xy ) 7 = 1. Every such group G is the conformal automorphism group of some compact Riemann surface of genus g > 1, with the property that | G | = 84( g – 1), which is the maximum possible order for given genus g . This paper provides an update on what is known about Hurwitz groups and related matters, following up the author's brief survey in Bull. Amer. Math. Soc. 23 (1990). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Groups - Complexity - Cryptology de Gruyter

An update on Hurwitz groups

Conder, Marston
Groups - Complexity - Cryptology , Volume 2 (1) – Jun 1, 2010
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Publisher
de Gruyter
Copyright
Copyright © 2010 by the
ISSN
1867-1144
eISSN
1869-6104
DOI
10.1515/gcc.2010.002
Publisher site
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Abstract

Abstract A Hurwitz group is any non-trivial finite quotient of the (2, 3, 7) triangle group, that is, any non-trivial finite group generated by elements x and y satisfying x 2 = y 3 = ( xy ) 7 = 1. Every such group G is the conformal automorphism group of some compact Riemann surface of genus g > 1, with the property that | G | = 84( g – 1), which is the maximum possible order for given genus g . This paper provides an update on what is known about Hurwitz groups and related matters, following up the author's brief survey in Bull. Amer. Math. Soc. 23 (1990).

Journal

Groups - Complexity - Cryptology – de Gruyter

Published: Jun 1, 2010

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