Cameron's integral-domain conjecture for permutation group algebras

Let $G$ be a permutation group on an infinite set $\Omega$, and let $A(G)$ be Cameron's commutative, associative, graded algebra encoding the action of $G$ on finite subsets of $\Omega$.

Cameron's integral-domain conjecture. If $G$ has no finite orbits, then $A(G)$ is an integral domain.

This is the weaker of two conjectures discussed by the paper and would establish that the permutation group algebra has no zero divisors under the stated orbit condition. The paper says that the conjecture is proved in certain special cases, including specified wreath-product cases, but gives no general resolution.