Conjugacy class
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Revision 741
7/31/2026, 9:35:35 AM · Sequoia
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Recorded titleConjugacy class
Recorded typeDefinition
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A conjugacy class is...1
A conjugacy class of an element $x$ from a [[Group|group]] $(G,\cdot)$ is the set $\{gxg^{-1}, g\in G\}$.2
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It can also be viewed as the [[Orbit of a group action|orbit]] of $x$ under the [[Group action|action]] $(g,x)\in G\times X\longmapsto gxg^{-1}\in X$ of $G$ over $X:=G$.Revision 129
6/28/2026, 8:57:31 AM · Ancient Tree
Concept created
A conjugacy class is...