An **alternating group**, denoted \( A_n \), is a specific type of group in the field of abstract algebra. It consists of all the even permutations of a finite set of \( n \) elements. To fully understand this concept, it's important to break down a few terms: 1. **Permutation**: A permutation of a set is a rearrangement of its elements.
Note that odd permutations don't form a subgroup of the symmetric group like the even permutations do, because the composition of two odd permutations is an even permutation.
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