Let \(\displaystyle p\) be a prime number. We define the frobenius group by
\(\displaystyle F_{p(p-1}=\left\{\begin{pmatrix}a&b\\0&1\end{pmatrix}, a\in \mathbb{F}_p^{\times}, b\in \mathbb{F}_p\right\}\)
I want to identify the center \(\displaystyle Z(F_{p(p-1)})\) and \(\displaystyle F'_{p(p-1)}=[F_{p(p-1)}:F_{p(p-1)}]\)
with I will be gratefull if you could help me.
\(\displaystyle F_{p(p-1}=\left\{\begin{pmatrix}a&b\\0&1\end{pmatrix}, a\in \mathbb{F}_p^{\times}, b\in \mathbb{F}_p\right\}\)
I want to identify the center \(\displaystyle Z(F_{p(p-1)})\) and \(\displaystyle F'_{p(p-1)}=[F_{p(p-1)}:F_{p(p-1)}]\)
with I will be gratefull if you could help me.
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