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Collecting proofs that finite multiplicative subgroups of fields are cyclic

For the field ${\bf{Z}}/(p)$, we can argue this way. Suppose there is $K\le({\bf{Z}}/(p))^\times$ such that $K\cong C_q\times C_q$, for some prime $q$. Therefore, there are $q^2-1$ distinct elements $...

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