= Centralizer of a subset
{title2=$C_G(A)=\bigcap_{a\in A}C_G(a)$}
The centralizer of a subset $A$ of a <group> consists of the elements commuting with every member of $A$. It is the intersection of the element <centralizers>, hence a <subgroup>. Directly, identity commutes with every element, products of two elements that each commute with every member of $A$ still have that property, and the same is true of inverses. For $A=G$ this is the <centre of a group>. For an empty subset the commutation condition is vacuous and the centralizer is all of $G$.
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