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 Th17:
  for Gc, Hc being strict finite cyclic Group st card Hc = card Gc
  holds Hc,Gc are_isomorphic
proof
  let Gc, Hc be strict finite cyclic Group;
  set p = card Hc;
  assume card Hc = card Gc;
  then
A1: INT.Group(p),Gc are_isomorphic by Th15;
  INT.Group(p),Hc are_isomorphic by Th15;
  hence thesis by A1,GROUP_6:67;
end;
