(* (c) Copyright 2006-2016 Microsoft Corporation and Inria.                  *)
(* Distributed under the terms of CeCILL-B.                                  *)
From mathcomp
From mathcomp
From mathcomp
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(*   The Sylow theorem and its consequences, including the Frattini argument, *)
(* the nilpotence of p-groups, and the Baer-Suzuki theorem.                   *)
(*   This file also defines:                                                  *)
(*      Zgroup G == G is a Z-group, i.e., has only cyclic Sylow p-subgroups.  *)
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Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
(* The mod p lemma for the action of p-groups. *)
Section ModP.
Variable (aT : finGroupType) (sT : finType) (D : {group aT}).
Variable to : action D sT.

Lemma pgroup_fix_mod (p : nat) (G : {group aT}) (S : {set sT}) :
p.-group G -> [acts G, on S | to] -> #|S| = #|'Fix_(S | to)(G)| %[mod p].