**Corollary 11.1.1**: *If q is a prime, then all star flocks of thick cones are linear.*

*Pf*: The cases of q = 2 (Proposition 4.1 ) and q = 3 (Proposition 9.1 ) have already been dealt with. So, we may assume that q is a prime > 3. Since a prime field has no proper subfields, there are no p^{e}-linearized polynomials other than the linear ones, so by Theorem 11.1.3 there are no proper star flocks.