# Thread: finite symmetric group HELP..

1. ## finite symmetric group HELP..

hi there..

i just learnt about some simple group theory

would like to seek for answer on some questions i have on the symmetric group ( had questions about it on exercise but was not formally taught)..

what exactly is a symmetric group?

can anyone help give an example of the bijection in a symmetric group?

is it supposed to be a function?

explain and proof maybe why a symmetric group has order n! ?

and if possible provide any references for beginners?

Thank you very much...

2. Let $S$ be a finite non-empty set. We say $\tau$ is a permutation when $\tau: S\mapsto S$ is a one-to-one onto map (i.e. a bijection). Let $\mbox{Sym}(S)$ be the set of all permutations. Then $\mbox{Sym}(S)$ is a group under function composition. This group is called symettric group.