The alternating group is a group consisting of all even permutations of a set of elements. An even permutation is one that can be written as a combination of an even number of transpositions. This group is a subgroup of the symmetric group, which includes all possible permutations. The alternating group has half the elements of the symmetric group. For five or more elements, the alternating group is simple, meaning it has no non-trivial subgroups. It is also non-abelian, meaning the order of operations matters.
