reserve X for set;
reserve G for Group;
reserve H for Subgroup of G;
reserve h,x,y for object;
reserve f for Endomorphism of G;
reserve phi for Automorphism of G;
reserve K for characteristic Subgroup of G;

theorem
  G` is characteristic
proof
  A1: [.1_G,1_G.] in commutators G;
  for phi being Automorphism of G holds phi .: commutators G = commutators G
  by Th43;
  hence thesis by A1,Th45;
end;
