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A Note on Torsion Free Groups Generated by Pairs of Matrices

Published online by Cambridge University Press:  20 November 2018

A. Charnow
A. Charnow*
Affiliation:
Department of Mathematics, California State University, Hayward, California 94542
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Let and let Gm be the group generated by A and the transpose of A. The problem of determining complex numbers m such that Gm is a free group had been studied by several authors [1, 2, 3]. In this note we characterize those rational values of m for which Gm is torsion free.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 5 , February 1975 , pp. 747 - 748
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Brenner, J. L., Quelques groupes libres de matrices, C. R. Acad. Sci. Paris 241 (1955), 1689- 1691.Google Scholar
2. Chang, B., Jennings, S. A., and Ree, R., On certain matrices which generate free groups, Can. J. Math. 10 (1958), 279–284.Google Scholar
3. Lyndon, R. C. and Ullman, J. L., Groups generated by two parabolic linear fractional transformations, Can. J. Math. 21 (1969), 1388–1403.Google Scholar