My understanding is that in general, the decomposition of a module into various forms (e.g. into cyclic modules by the elementary divisor method) is not unique because there may be non-trivial automorphisms of the module. However, some spaces are canonical, e.g. the torsion submodule. My question is: is the p-primary component of a module (i.e. the submodule of elements annihilated by some power of the prime p) canonical?