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Homomorphism from GL(2,N) to Z_N?

  1. May 5, 2013 #1
    I start with the group GL(2,N), where N is prime. I want to break these elements into N classes. One way to do this would be to find a homomorphism to Z_N, does such a homomorphism exist for general N? What is it? Is there another way to break the group into classes without using a homomorphism?
  2. jcsd
  3. May 5, 2013 #2


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    If the notation GL(2,N) means that this group acts on a vector space of indefinite inner product, then there is a natural SL(N) subgroup. The center of this subgroup is ##\mathbb{Z}_N##.
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