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Presentations of some classical groups

Published online by Cambridge University Press:  17 April 2009

M.J. Wicks
M.J. Wicks
Affiliation:
Department of Mathematics, University of Singapore, Singapore.
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Abstract

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The groups considered are Λ = GL(2, Z), π = SL(2, Z) and Θ = PSL(2, Z). A presentation of Λ is obtained for which the word problem can be solved by a simple intrinsic algorithm. The presentation is modified to display other features of Λ, and to obtain related presentations of Λ and Θ. There is an algorithm which solves the conjugacy problem of Λ.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 13 , Issue 1 , August 1975 , pp. 1 - 12
Copyright
Copyright © Australian Mathematical Society 1975

References

[1]Cohn, Harvey, “Markoff forms and primitive words”, Math. Ann. 196 (1972), 8–22.CrossRefGoogle Scholar
[2]Coxeter, H.S.M. and Moser, W.O.J., Generators and relations for discrete groups (Ergebnisse der Mathematik und ihrer Grenzgebiete, 14. Springer-Verlag, Berlin, Gottingen, Heidelberg, 1957; 3rd ed, 1972).CrossRefGoogle Scholar
[3]Newman, Morris, Integral matrices (Pure and Applied Mathematics, 45. Academic Press, New York and London, 1972).Google Scholar
[4]Wicks, M.J., “A general solution of binary homogeneous equations over free groups”, Pacific J. Math. 41 (1972), 543–561.CrossRefGoogle Scholar