= Finitely generated subgroup of the rational additive group
{title2=$\langle a_1/d,\ldots,a_k/d\rangle=(\gcd(a_1,\ldots,a_k)/d)\mathbb Z$}
A nonzero finitely generated <subgroup> of the additive <rational numbers> is an <infinite cyclic group>. Put the generators over a common positive denominator. Their integer numerators generate the ideal given by their <greatest common divisor>, and <Bezout identity> expresses that divisor as an integer combination of them. Dividing back by the denominator gives a single generator.
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