Section Primitive.
Variables (aT : finGroupType) (sT : finType).
Variables (G : {group aT}) (to : {action aT &-> sT}) (S : {set sT}).

Lemma prim_trans_norm (H : {group aT}) :
[primitive G, on S | to] -> H <| G ->
H \subset 'C_G(S | to) \/ [transitive H, on S | to].