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

From Groupprops

## Statement

### For alternating groups on finite sets

Suppose is a natural number satisfying . Then the Alternating group (?) is a 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 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.