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Some results on quotients of triangle groups

Published online by Cambridge University Press:  17 April 2009

Marston D.E. Conder
Marston D.E. Conder
Affiliation:
Department of Mathematics and Statistics, University of Auckland, Private Bag, Auckland, New Zealand.
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Abstract

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Given positive integers k, l, m, the (k, l, m) triangle group has presentation δ(k, l, m) = < X, Y, Z | Xk = Yl = Zm = XYZ = 1 >. This paper considers finite permutation representations of such groups. In particular it contains descriptions of graphical and computational techniques for handling them, leading to new results on minimal two-element generation of the finite alternating and symmetric groups and the group of Rubik's cube. Applications to the theory of regular maps and automorphisms of surfaces are also discussed.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 30 , Issue 1 , August 1984 , pp. 73 - 90
Copyright
Copyright © Australian Mathematical Society 1984

References

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