Section ModularGroupAction.
Variables (aT rT : finGroupType) (D : {group aT}) (R : {group rT}).
Variables (to : groupAction D R) (p : nat).
Implicit Types (G H : {group aT}) (M : {group rT}).

Lemma nontrivial_gacent_pgroup G M :
p.-group G -> p.-group M -> {acts G, on group M | to} ->
M :!=: 1 -> 'C_(M | to)(G) :!=: 1.