Show that Q, the group of rational numbers under addition, has no proper subgroups of finite index, but Z has.
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Originally Posted by mandy123 Show that Q, the group of rational numbers under addition, has no proper subgroups of finite index, but Z has. let N be a subgroup of with since is abelian, N is normal and hence is a group of order so: thus: is this really not in your lecture notes that every nonzero subgroup of has finite index?!!!
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