# Category:Normalizers

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This category contains results about **Normalizers**.

Let $G$ be a group.

Let $S$ be a subset of $G$.

Then the **normalizer of $S$ in $G$** is the set $\map {N_G} S$ defined as:

- $\map {N_G} S := \set {a \in G: S^a = S}$

where $S^a$ is the $G$-conjugate of $S$ by $a$.

## Subcategories

This category has the following 3 subcategories, out of 3 total.

## Pages in category "Normalizers"

The following 17 pages are in this category, out of 17 total.

### N

- Normal Subgroup iff Normalizer is Group
- Normalizer is Subgroup
- Normalizer of Center is Group
- Normalizer of Conjugate is Conjugate of Normalizer
- Normalizer of Reflection in Dihedral Group
- Normalizer of Rotation in Dihedral Group
- Normalizer of Subgroup is Largest Subgroup containing that Subgroup as Normal Subgroup
- Normalizer of Subgroup of Symmetric Group that Fixes n
- Normalizer of Sylow p-Subgroup
- Number of Distinct Conjugate Subsets is Index of Normalizer