Identity of Group is in Singleton Conjugacy Class

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Let $G$ be a group.

Let $e$ be the identity of $G$.

Then $e$ is in its own singleton conjugacy class:

$\conjclass e = \set e$


From Identity of Group is in Center:

$e \in \map Z G$

where $\map Z G$ is the center of $G$.

From Conjugacy Class of Element of Center is Singleton:

$\conjclass e = \set e$