Category:Definitions/Centralizers

This category contains definitions related to Centralizers.
Related results can be found in Category:Centralizers.

Let $\struct {G, \circ}$ be a group.

Let $a \in \struct {G, \circ}$.

The centralizer of $a$ (in $G$) is defined as:

$\map {C_G} a = \set {x \in G: x \circ a = a \circ x}$

That is, the centralizer of $a$ is the set of elements of $G$ which commute with $a$.