  In a quaternion order of class number one, an element can be factored in
multiple ways depending on the order of the factorization of its reduced norm.
The fact that multiplication is not commutative causes an element to induce a
permutation on the set of primes of a given reduced norm. We discuss this
permutation and previously known results about the cycle structure, sign, and
number of fixed points for quaternion orders. We generalize these results to
other orders in central simple algebras over global fields.
