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Math Help - finite symmetric group HELP..

  1. #1
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    Post 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...
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  2. #2
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    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.
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