Subgroup of an infinite cyclic group
= Subgroup of an infinite cyclic group
= Subgroups of an infinite cyclic group
{synonym}
For $G=\langle g\rangle$ infinite, every <subgroup> is $\langle g^m\rangle$ for a unique integer $m\geq0$. This is the classification of subgroups of the <additive group of integers> transported through a <group isomorphism>. For $m>0$ the <subgroup index> is $m$ and the subgroup is again an <infinite cyclic group>; for $m=0$ it is trivial and has infinite <subgroup index>.