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Let $p$ be a prime number. The order of a $p$-Sylow subgroup of the group $GL_{50}(\mathbb{F}_p)$ of invertible $50×50$ matrices with entries from finite field $\mathbb{F}_p$ equals:
$p^{50}$
$p^{125}$
$p^{1250}$
$p^{1225}$

I am completely stuck on it.can anyone help me please.

  • 0
    To exclude some alternatives you may want to calculate the order of the subgroup of upper triangular matrices with 1s along the diagonal.2012-12-16

2 Answers 2