Hostname: page-component-77c89778f8-gq7q9 Total loading time: 0 Render date: 2024-07-22T18:26:14.316Z Has data issue: false hasContentIssue false
  • English
  • Français

Subgroups of SL2ℤ generated by elementary matrices

Published online by Cambridge University Press:  14 November 2011

Randy Tuler
Randy Tuler
Affiliation:
Department of Mathematics, University of Georgia, Athens, Georgia 30602, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Synopsis

An elementary matrix has ones down the main diagonal and at most one element off the diagonal that differs from zero. We study the subgroups of SL2ℤ generated by sets of elementary matrices. Specifically, we give a stringent condition that the entries of a matrix belonging to such a group must satisfy.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 88 , Issue 1-2 , 1981 , pp. 43 - 47
Copyright
Copyright © Royal Society of Edinburgh 1981

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Tuler, R.. Arithmetic sums that determine linear characters on Г(N). Pacific J. Math. 89 (1980), in press.Google Scholar
2Tuler, R.. Topological construction of multiplier systems on Г(N) (Dissertation, Univ. of California, Berkeley, 1979).Google Scholar
3Borevich, Z. I. and Shafarevich, I. R.. Number Theory (New York: Academic Press, 1966).Google Scholar
4Rademacher, H. and Grosswald, E.. Dedekind Sums. The Carus Mathematical Monographs, no. 16 (Washington, D.C.: The Mathematical Association of America).Google Scholar
5Hirzebruch, F. and Zagier, D.. The Atiyah-Singer Theorem and Elementary Number Theory (Publish or Perish, 1974).Google Scholar
6Cohn, P.. On the structure of GL2 of a ring. Inst. Hautes Études Sci. Publ. Math. 30 (1966), 5–53.CrossRefGoogle Scholar