# Category:Symmetric Groups

This category contains results about Symmetric Groups.
Definitions specific to this category can be found in Definitions/Symmetric Groups.

Let $S$ be a set.

Let $\map \Gamma S$ denote the set of permutations on $S$.

Let $\struct {\map \Gamma S, \circ}$ be the algebraic structure such that $\circ$ denotes the composition of mappings.

Then $\struct {\map \Gamma S, \circ}$ is called the symmetric group on $S$.

If $S$ has $n$ elements, then $\struct {\map \Gamma S, \circ}$ is often denoted $S_n$.

## Subcategories

This category has the following 17 subcategories, out of 17 total.