| Version 3 |
Version 2 |
| Let $X$ be a set. |
Let $X$ be a set. |
| Let $S(X)$ be the set of permutations of $X$ |
Let $S(X)$ be the set of permutations of $X$ |
| (i.e. the set of bijective functions on $X$). |
(i.e. the set of bijective functions on $X$). |
| Then the act of taking the composition of two permutations |
Then the act of taking the composition of two permutations |
| induces a group structure on $S(X)$. |
induces a group structure on $S(X)$. |
| We call this group the {\it symmetric group} |
We call this group the {\it symmetric group} |
|
or the {\it permutation group} on $X$, |
| and it is often denoted ${\rm Sym}(X)$. |
and it is often denoted ${\rm Sym}(X)$. |
