Paper 3, Section I, D

Groups | Part IA, 2014

Let G=QG=\mathbb{Q} be the rational numbers, with addition as the group operation. Let x,yx, y be non-zero elements of GG, and let NGN \leqslant G be the subgroup they generate. Show that NN is isomorphic to Z\mathbb{Z}.

Find non-zero elements x,yRx, y \in \mathbb{R} which generate a subgroup that is not isomorphic to Z\mathbb{Z}.

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