Notes - Galois Theory HT25, Groups
Flashcards
@Define the sign of a permutation $\sigma \in S _ n$.
\[\begin{aligned}
\text{sgn} &: S_n \to \pm 1 \\\\
\sigma &\mapsto \begin{cases}
1 &\text{if } \sigma \in A_n \\\\
-1 &\text{if } \sigma \notin A_n
\end{cases}
\end{aligned}\]
@State the automorphisms of $\mathbb Z / n \mathbb Z$.
\[\text{Aut}(\mathbb Z / n \mathbb Z) \cong (\mathbb Z / n \mathbb Z)^\times\]