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INFINITE SIMPLE (2, 3, n)-GROUPS AND CONGRUENCE HULLS IN THE MODULAR GROUP

Published online by Cambridge University Press:  01 July 1999

A. W. MASON  and
S. J. PRIDE
A. W. MASON
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW
S. J. PRIDE
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW
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Abstract

We prove that if n>66 and (n, 30) = 1, then there exist uncountably many infinite simple (2, 3, n)-groups, that is, groups generated by a pair of elements x, y, say, where the orders of x, y and xy are 2, 3 and n, respectively. This extends previous results of Schupp and the authors.

These results are used to prove the existence of subgroups of the modular group with special arithmetic properties.

Information

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 31 , Issue 4 , July 1999 , pp. 450 - 456
Copyright
© The London Mathematical Society 1999

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