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On Certain Pairs of Matrices which Generate free Groups

Published online by Cambridge University Press:  20 November 2018

Bomshik Chang ,
S. A. Jennings  and
Rimhak Ree
Bomshik Chang
Affiliation:
University of British Columbia
S. A. Jennings
Affiliation:
University of British Columbia
Rimhak Ree
Affiliation:
University of British Columbia
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Denote by Fα,β the multiplicative group generated by the two matrices where α and β are complex numbers. Sanov (3) proved that Fα,β is free, and Brenner (1) showed that Fm,m is free if m ⩾ 2.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 279 - 284
Copyright
Copyright © Canadian Mathematical Society 1958 

Footnotes

This research was in part supported by National Research Council of Canada grant G. 489.

References

1. Brenner, J. L., Quelques groupes libres de matrices, C. R. Acad. Sci. Paris 241 (1955), 1689-1691.Google Scholar
2. Goldberg, K. and Newman, M., Pairs of matrices of order two which generate free groups, 111. J. Math. 1 (1957), 446-448.Google Scholar
3. Sanov, I. N., A property of a representation of a free group, Doklady Akad. Nauk (N.S.) 57 (1947), 657-659.Google Scholar
4. van, B. L. der Waerden, Modern algebra, vol. 1 (New York, 1949).Google Scholar