I was looking over Alperin's Local Representation Theory and I realized I remembered a definition that may not be there (or true).
Is a relatively H-free G-module exactly the same as a G-module isomorphic to an induced H-module?
Lemma 8.4 on page 56 shows that induced modules are relatively H-free, and the other direction seems like some sort of restatement of Frobenius reciprocity, but since the book doesn't mention the equivalence, I worry it is not true.