Extend finite-generation of cohomology to arbitrary Noetherian coefficient rings

Establish whether the cohomology algebra H*(G;k) of a locally finite Artinian group G is finitely generated as a k-algebra for every commutative Noetherian ring k, extending the established result for coefficients in the field F_p.

Background

The paper proves that for a locally finite Artinian group G, the mod-p cohomology ring H*(G;F_p) is a finitely generated F_p-algebra. The authors then identify the analogous statement over an arbitrary commutative Noetherian coefficient ring as unresolved.

The question concerns whether the finite-generation property depends on using a field of characteristic p or persists for all commutative Noetherian base rings. The authors indicate that they expect the result to remain true in this broader setting, but do not establish it.