Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-06-08T11:35:37.461Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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