Cameron's prime-element 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 $\Omega$. Let $\varepsilon$ be the element of the degree-one component defined in the paper.

Cameron's prime-element conjecture. If $G$ has no finite orbits, then $\varepsilon$ is a prime element in $A(G)$.

This is one of Cameron's conjectures concerning zero divisors in permutation group algebras. The paper presents it as the stronger of two conjectures and indicates that the weaker integral-domain conjecture follows from it; its general status is not specified here.