 reserve G, A for Group;
 reserve phi for Homomorphism of A,AutGroup(G);
 reserve G, A for Group;
 reserve phi for Homomorphism of A,AutGroup(G);
reserve G1,G2 for Group;

theorem Th73:
  G is strict trivial implies semidirect_product(G,A,phi), A are_isomorphic
proof
  assume A1: G is strict trivial;
  then AutGroup G is trivial by Th70;
  then phi = 1:(A,AutGroup G) by Th68;
  then semidirect_product(G,A,phi) = product <*G,A*> by Th38;
  hence semidirect_product(G,A,phi), A are_isomorphic by A1,Th72;
end;
