Even permutation

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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