Even permutation

Definition
An even permutation is a permutation on a finite set (equivalently, a finitary permutation on a possibly infinite set) satisfying the following equivalent conditions:


 * 1) It can be expressed as a product of an even number of transpositions.
 * 2) The number of cycles of even length in its cycle decomposition is even.
 * 3) It is in the alternating group (respectively, the finitary alternating group) on the set.

Related properties

 * Odd permutation
 * Finitary permutation