Braid Groups pp 311-314 | Cite as

Presentations of SL2(Z) and PSL2(Z)

Part of the Graduate Texts in Mathematics book series (GTM, volume 247)

Let \(\textrm{SL}_2({\bf Z})\) be the group of \(2 \times 2\) matrices with entries in \({\bf Z}\) and with determinant 1. The center of \(\textrm{SL}_2({\bf Z})\) is the group of order 2 generated by the scalar matrix \(-I_2\), where I 2 is the unit matrix. The quotient group
$$\textrm{PSL}_2({\bf Z}) = \textrm{SL}_2({\bf Z})/\langle -I_2 \rangle$$
is called the modular group; it can be identified with the group of rational functions on \({\bf C}\) of the form \((az+b)/(cz+d)\), where a, b, c, d are integers such that \(ad - bc = 1\).


Rational Function Unit Matrix Group Theory Algebraic Structure Cell Complex 

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© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Institut de Recherche Mathématique Avancée, CNRS et Université Louis PasteurStrasbourgFrance
  2. 2.Department of MathematicsIndiana University BloomingtonBloomingtonUSA

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