Group with no center

  • Thread starter arz2000
  • Start date
  • #1
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Main Question or Discussion Point

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?

Regards
 

Answers and Replies

  • #2
15
0
I mean all 3 by 3 matrices with the following rows
(e^t, 0, u)
(0, e^(tx), v)
(0, 0, 1).
 
  • #3
matt grime
Science Advisor
Homework Helper
9,395
3
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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