Bulletin of the Australian Mathematical Society

Research Article

A family of Hurwitz groups with non-trivial centres

Marston Condera1

a1 Department of Mathematics and Statistics, University of Auckland, Private Bag, Auckland, New Zealand.

Abstract

In this paper a new family of quotients of the triangle group < x, y, z | x2 = y3 = z7 = xyz = 1 > is obtained. It is shown that for every positive integer m divisible by 3 there is a Hurwitz group of order 504m6 having a centre of size 3, and as a consequence there is a Riemann surface of genus 6m6 + 1 with the maximum possible number of automorphisms.

(Received May 27 1985)