The equivalence of some conjectures of Dade and Robinson

We demonstrate that Conjecture 4.1 of [G.R. Robinson, Proc. London Math. Soc. (3) 72 (1996) 312–330] and Dadeʹs projective conjecture are equivalent in a way which is compatible with the p-local rank. Further we consider refinements of these conjectures similar to those of Isaacs, Navarro and Uno, show their equivalence and demonstrate that in order to verify them it suffices to consider only those groups with no non-central normal p-subgroup.