# Category:Centers of Groups

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This category contains results about **Centers of Groups**.

The **center of a group** $G$, denoted $\map Z G$, is the subset of elements in $G$ that commute with every element in $G$.

Symbolically:

- $\map Z G = \map {C_G} G = \set {g \in G: g x = x g, \forall x \in G}$

That is, the **center** of $G$ is the centralizer of $G$ in $G$ itself.

## Subcategories

This category has the following 4 subcategories, out of 4 total.

### C

- Center of Group is Subgroup (3 P)

## Pages in category "Centers of Groups"

The following 25 pages are in this category, out of 25 total.

### C

- Center is Characteristic Subgroup
- Center is Intersection of Centralizers
- Center of Dihedral Group
- Center of Dihedral Group D4
- Center of Group is Abelian Subgroup
- Center of Group is Kernel of Conjugacy Action
- Center of Group is Normal Subgroup
- Center of Group is Subgroup
- Center of Group of Order Prime Cubed
- Center of Group of Prime Power Order is Non-Trivial
- Center of Non-Abelian Group of Order pq is Trivial
- Center of Opposite Group
- Center of Quaternion Group
- Center of Symmetric Group is Trivial
- Conjugacy Class of Element of Center is Singleton