Several groups have the property that every element is its own inverse. For example, the numbers $0$ and $1$ and the XOR operator form a group of this sort, and more generally the set of all bitstrings of length n and XOR form a group with this property.
These groups have the interesting property that they have to be commutative.
Is there a special name associated with groups with this property? Or are they just "abelian groups where every element has order two?"