Symmetric Group on $X$

Please Login to access more options.

Definition (Symmetric Group on $X$)

Let $X$ be any set. The $\textdef{symmetric group}$ on $X$, denoted $\sym(X)$, is the set of all permutations of $X$. We denote by $S_n$ the symmetric group on $X = \{1,2,\ldots, n\}$ and call it the symmetric group of degree $n$.

The following pages link to this page.