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Group with no center

  1. Mar 16, 2007 #1
    Hi all,
    can you show that the group of all 3 by 3 matrices
    [e^t 0 u
    0 e^xt v
    0 0 1]
    where t, u, v are in C (complex numbers) and x is in R (real number)
    has no center?

  2. jcsd
  3. Mar 16, 2007 #2
    I mean all 3 by 3 matrices with the following rows
    (e^t, 0, u)
    (0, e^(tx), v)
    (0, 0, 1).
  4. Mar 16, 2007 #3

    matt grime

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    Science Advisor
    Homework Helper

    You can't, since it does have a centre - every group has a centre, possibly trivial (as it is in this case).

    You just write down two matrices, suppose the commute and show that this implies that they are both the identity matrix.
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