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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.

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

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