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How can I find the subgroups of abelian group $\mathbb{Z}_5$?

From Lagrange's theorem, the size of the subgroup should divide 5 in this case. So the size of the subgroup should be 1 or 5 ($\mathbb{Z}_5$ itself). Can there be any size 1 subgroups of $\mathbb{Z}_5$?

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    **Every** group has one and only one subgroup of size $1$: the subgroup that consists only of the identity element of the group.2012-04-21

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