where $T_n(F_p)$ denotes the the group of $n \times n$ invertible upper triangular matrices with entries in the field $F_p$ and $p$ is a prime. $O_3(F_2)$ is the orthogonal group. $SO_3(F_3)$ stands for the special orthogonal group. $SL_3(F_p)$ stands for the special linear group.
How to calculate the orders of these groups: $T_n(F_p) , SL_3(F_p) , O_3(F_2) , SO_3(F_3) , O_2(F_7)$
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group-theory
representation-theory
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0First off, you should make the question self-contained, *without* relying on the title. Second, issuing commands like this, with no reference to any work *you yourself* have done, is unlikely to elicit lots of answers. – 2012-02-20
1 Answers
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Partial answer: For SL(n), the Bruhat decomposition makes it very easy.