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Unformatted text preview: special linear group , consists of the matrices with determinant 1. The projective versions of these groups are obtained by taking the quotient with their respective centers (scalars of the identity matrix). That is, PGL 2 ( R ) = GL 2 ( R ) / h cI i , PGL + 2 ( R ) = GL + 2 ( R ) / h cI i , PSL 2 ( R ) = SL 2 ( R ) / { I } . (a) Prove that the center of the general linear group, Z (GL 2 ( R )) = h cI  c R i , is a subset (and hence a a subgroup) of GL + 2 ( R ). (b) Prove that PGL + 2 ( R ) is isomorphic to PSL 2 ( R ). [ Hint : Use the rst isomorphism theorem if : G H is a homomorphism, then G/ ker = im .] MthSc 481  Topics in Geometry and Topology  Spring 2012  M. Macauley...
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This note was uploaded on 03/11/2012 for the course MTHSC 481 taught by Professor Staff during the Spring '12 term at Clemson.
 Spring '12
 Staff
 Geometry, Topology

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