Symmetric Group On N Letters

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Formal Definition

Let $A$ be the finite set $\{1,2,\cdots ,n\}$.The group of all permutations of A is the symmetric group on n letters, and is denoted by $S_n$.

Informal Definition

The symmetric group on n letters is the group of elements that are all the different rearrangements of the n symbols.


Let $A=\{1,2\}$.For $S_2$, $\begin{pmatrix}1&2\\1&2\end{pmatrix}$ and $\begin{pmatrix}1&2\\2&1\end{pmatrix}$ are the permutations of set $A$.


Let $A=\{1,2,3\}$. For $S_3$, $\begin{pmatrix}1&2&3\\3&3&1\end{pmatrix}$ would not be a part of the set because it is not permutation of set $A$.

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