reserve F,G for Group;
reserve G1 for Subgroup of G;
reserve Gc for cyclic Group;
reserve H for Subgroup of Gc;
reserve f for Homomorphism of G,Gc;
reserve a,b for Element of G;
reserve g for Element of Gc;
reserve a1 for Element of G1;
reserve k,m,n,p,s for Element of NAT;
reserve i0,i,i1,i2 for Integer;
reserve j,j1 for Element of INT.Group;
reserve x,y,t for set;

theorem Th18:
  for F,G being strict finite Group st card F = p & card G = p & p
  is prime holds F,G are_isomorphic
proof
  let F,G be strict finite Group;
  assume that
A1: card F = p & card G = p and
A2: p is prime;
  F is cyclic Group & G is cyclic Group by A1,A2,GR_CY_1:21;
  hence thesis by A1,Th17;
end;
