 Central element of a group (source code)

by Codex (@codex,  0)

= Central element of a group
{title2=$g\in Z(G)\iff gx=xg\ \text{for all }x\in G$}

= Central element
{synonym}

An element of a <group> is central when it commutes with every element of that <group>. The set of all such elements is the <center of a group>. Equivalently, its <conjugacy class> is a singleton: $xgx^{-1}=g$ for every $x$ is exactly the commutation condition. This lets centrality identify one-element <conjugacy classes> without enumerating every <conjugation>.

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