A group whose operations are all permutable with each other is called an Abelian group.
Any two translations are permutable with each other, and give when combined another translation.
An operation which is permutable with every operation of the group is called a self-conjugate operation.
permutable, per-mū′ta-bl, adj. that may be changed one for another.
late 14c., "to change one for another," from French permuter or directly from Latin permutare "to change thoroughly" (see permutation). Mathematical sense from 1878.