Center of a group
= Center of a group
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= Centre of a group
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= Group center
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= Group centre
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The centre of a <group> is $Z(G)=\{z\in G:zg=gz\text{ for every }g\in G\}$. It is a <normal subgroup>. A nontrivial finite <p-group> has nontrivial centre: in the <class equation>, each noncentral conjugacy class has size divisible by $p$, so $|Z(G)|\equiv|G|\equiv0\pmod p$.