Question

prove that any finitely generated subgroup (Q,+) is cyclic ​

Answer 1

Step-by-step explanation:

〉 and hence H is cyclic itself. This proves the claim that every finitely generated subgroup of Q is cyclic. ... For example, 〈(1, 0), (0, 1)〉 = Z × Z is finitely generated but not cyclic. This implies that the groups Q and Q × Q are not isomorphic.