##  [Alternating Group](/alternating-group) 

  ##  [Alternating Group](https://algebra.quantumdictionary.io/alternating-group-0) 

  

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**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The Alternating Group A_n is the subgroup of the symmetric group S_n consisting of all even permutations (those expressible as an even number of transpositions); it is of index two in S_n and has order n!/2 for n ≥ 2.