This generalizes to convolution in an arbitrary group (and even groupoid, and even category), not necessarily one that is commutative like the reals or integers are. For group convolution over a group G, the functions take values in the complex numbers and have domain the elements of G. The value of the convolution of two such functions f and g at a point c (a group element) is computed by taking the sums f(a)*g(b) where ab = c.

This has applications in quantum mechanics where non-commutativity plays a prominent role.