Permutation of a set

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Note: permutation on a set redirects here.

Definition

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

Claims:

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.

References

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