= Two generators for elliptic curves over finite fields
{title2=$E(\mathbb F_q)\cong\mathbb Z/m\mathbb Z\times\mathbb Z/n\mathbb Z$}
For an <elliptic curve> over a finite field of characteristic $p$, its rational-point group is finite and abelian. <Prime-to-characteristic geometric torsion> bounds every other prime-torsion dimension by two. Multiplication by $p$ has degree $p^2$ and inseparable degree at least $p$, so the $p$-torsion dimension is at most one. The structure theorem for <finite abelian groups> therefore gives two cyclic factors with $m\mid n$ and $p\nmid m$.
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