let G, F be strict Group; :: thesis: ( G,F are_isomorphic & G is cyclic implies F is cyclic )
assume that
A1: G,F are_isomorphic and
A2: G is cyclic ; :: thesis: F is cyclic
consider h being Homomorphism of G,F such that
A3: h is bijective by A1, GROUP_6:def 11;
h is onto by A3, FUNCT_2:def 4;
then Image h = F by GROUP_6:57;
hence F is cyclic by A2, Th26; :: thesis: verum