Notes - Groups TT23, Group actions

Created: May 08, 2023
Updated: October 17, 2024

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• [[Course - Groups and Group Actions TT23]]^U

Flashcards

Define a left action of a group $G$ on a set $S$.

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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?

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$G$ acts on itself by

\[g \cdot h = ghg^{-1}\]

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