# Notes - Groups TT23, Group actions

> Source: https://ollybritton.com/notes/uni/prelims/tt23/groups/notes/group-actions/ · Updated: 2025-03-29 · Tags: uni, notes

- [Course - Groups and Group Actions TT23](https://ollybritton.com/notes/uni/prelims/tt23/groups/)

### Flashcards
@Define a left action of a group $G$ on a set $S$.::

A map
$$
\rho : G\times S \to S
$$
such that
1. $\rho(e, s) = s$ for all $s \in S$
2. $\rho(g, \rho(h, s)) = \rho(gh, s)$

Can you formulate conjugation as a group action?::

$G$ acts on itself by
$$
g \cdot h = ghg^{-1}
$$

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