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An update on Hurwitz groups
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Marston Conder
Published/Copyright:
June 23, 2010
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 x2 = y3 = (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).
Received: 2008-04-25
Published Online: 2010-06-23
Published in Print: 2010-June
© de Gruyter 2010
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- On Shephard groups with large triangles
- An update on Hurwitz groups
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Articles in the same Issue
- On Shephard groups with large triangles
- An update on Hurwitz groups
- Presentations of matrix rings
- The diameter of a random Cayley graph of ℤq
- Challenge response password security using combinatorial group theory
- The discrete logarithm problem in the group of non-singular circulant matrices
- Algebraic geometry over natural numbers. The classification of coordinate monoids
