2
$\begingroup$

I worked the proof for 3) in this link out, but I have problems with the last step:

Let $\sigma$ be a irred. representation of a normal subgroup $H=\langle z\rangle$ of $G$ and $\sigma'$ its dual representation. The proof comes to the conclusion that $\sigma \text { is equivalent to } \sigma' \Leftrightarrow z^{-1}=z^{p^k}, $ where $p$ is the charakteristic of the field $K$.

Where is the connection between saying that " $\sigma$ is equivalent to $\sigma'$ " and " $\sigma$ expands to a representation of $G$ "?

  • 0
    I've changed $$ to $\langle z\rangle$. The code for the former is ; that for the latter is \langle z\rangle.2012-08-27

0 Answers 0