Modified Group Non-Membership is in Promise-AWPP relative to group oracles.

It is known that the group non-membership problem is in QMA relative to any group oracle and in SPPnBQP for solvable groups. We consider a modified version of the group non-membership problem where the order of the group is also given as an additional input. We show that the problem is in (the promise version of) AWPP relative to any group oracle. To show the result, we use the idea of postselected quantum computing.