Groups TT23, Group actions
Flashcards
@Define a left action of a group $G$ on a set $S$.
A map
\[\rho : G\times S \to S\]such that
- $\rho(e, s) = s$ for all $s \in S$
- $\rho(g, \rho(h, s)) = \rho(gh, s)$
Can you formulate conjugation as a group action?
$G$ acts on itself by
\[g \cdot h = ghg^{-1}\]