Alternating group of degree at least five implies every element is a commutator

For alternating groups on finite sets
Suppose $$n$$ is a natural number satisfying $$n \ge 5$$. Then the fact about::alternating group $$A_n$$ is a fact about::group in which every element is a commutator has the property that every element of the group can be written as a commutator of two elements of the group. In other words, every even permutation on $$n$$ letters can be expressed as the commutator of two even permutations.

For finitary alternating groups on infinite sets
Any finitary alternating group on an infinite set is a group in which every element is a commutator.