Permutation of a set

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Stub grade: A*
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Very important to get some work on the symmetric group in play, then this may be demoted. Demote to grade A once the notation section has been added, there's a lot to say there.
Note: permutation on a set redirects here.


Let [ilmath]X[/ilmath] be any non-empty set, [ilmath]X[/ilmath]. A permutation on [ilmath]X[/ilmath][1][2] is:


The collection of all permutations of a set forms a group under function composition - see the permutation group. The symmetric group is a special case of the permutation group when the set is finite.


  1. Rings, Fields and Groups - An introduction to abstract algebra - R. B. J. T. Allenby
  2. Abstract Algebra - Pierre Antoine Grillet