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On Certain Pairs of Matrices which do not Generate a Free Group

Published online by Cambridge University Press:  20 November 2018

Rimhak Ree
Rimhak Ree*
Affiliation:
University of British Columbia
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A complex number λ will be said to be free if the multiplicative group Fλ generated by the two matrices

is a free group, and non-free, otherwise. Very little is known about the distribution of free and non-free numbers [1]. It is, for instance, unknown whether the domain

contains an open set which consists of only free points.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 4 , Issue 1 , January 1961 , pp. 49 - 52
Copyright
Copyright © Canadian Mathematical Society 1961

References

1. Chang, B., Jennings, S.A. and Ree, R., On certain pairs of matrices which generate free groups, Canad. J. Math. 10 (1958), 279-284.Google Scholar
2. Specht, W., Freie Untergruppen der binaren unimodularen Gruppe, Math. Z. 72 (1960), 319-331.Google Scholar