  Let C be a non-empty finite set, and Gamma a subgroup of the symmetric group
S(C). Given a bijection f:A cross C to B cross C, the problem of
Gamma-equivariant division is to find a quotient bijection h:A to B respecting
whatever symmetries f may have under the action of S(A) cross S(B) cross Gamma.
Say that Gamma is fully cancelling if this is possible for any f, and finitely
cancelling if it is possible providing A,B are finite. Feldman and Propp showed
that a permutation group is finitely cancelling just if it has a globally fixed
point. We show here that a permutation group is fully cancelling just if it is
trivial. This sheds light on the fact that all known division algorithms that
eschew the Axiom of Choice depend on fixing an ordering for the elements of C.
