# Category:Centralizers

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This category contains results about Centralizers.

Definitions specific to this category can be found in Definitions/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 $a$.

## Subcategories

This category has the following 2 subcategories, out of 2 total.

## Pages in category "Centralizers"

The following 10 pages are in this category, out of 10 total.