Naturalness of subgroup rank as a cohomological invariant

Determine whether the subgroup rank r_p(G) is a natural invariant for the group-cohomological applications in which sectional p-rank s_p(G) controls the dimension and complexity of group cohomology.

Background

The appendix introduces sectional p-rank s_p(G) and proves that sufficiently large sectional p-rank forces an elementary abelian subgroup of controlled rank. The authors note that sectional p-rank is used in group cohomology to control dimension and complexity.

They explicitly leave unresolved whether the ordinary subgroup rank r_p(G), which records only elementary abelian subgroups rather than elementary abelian subquotients, is likewise a natural invariant for those applications.