conjugacy class

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English

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conjugacy class

Noun

conjugacy class (plural conjugacy classes)

(algebra) A subset of a group which is an equivalence class in the quotient set of the group divided by conjugation as equivalence relation.
For a given element $x$ of some group $G$ , its conjugacy class $x^{G}$ is $\{y\in G|\exists g\in G:g^{-1}xg=y\}$ .

If a group acts on itself through conjugation, then its orbits are its conjugacy classes and its stabilizer subgroups are its centralizers.

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