Let be a finite non-empty set. We say is a permutation when is a one-to-one onto map (i.e. a bijection). Let be the set of all permutations. Then is a group under function composition. This group is called symettric group.
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...