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Free products of two real cyclic matrix groups

Published online by Cambridge University Press:  18 May 2009

R. J. Evans
R. J. Evans
Affiliation:
University of Wisconsin, Madison, Wisconsin 53706, U.S.A.
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We exhibit a large class K* of real 2 × 2 matrices of determinant ±1 such that, for nearly all A and B in K*, the group generated by A and B1 (the transpose of B) is the free product of the cyclic groups It is shown that K* contains all matrices of determinant ±1 with integer entries satisfying |b| > |a|, |c|, |d|. This gives a generalization of a theorem of Goldberg and Newman [2]. We also prove related results concerning the dominance of b and the discreteness of the free products .

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 15 , Issue 2 , September 1974 , pp. 121 - 128
Copyright
Copyright © Glasgow Mathematical Journal Trust 1974

References

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