Definition:Infinite Cyclic Group/Also known as
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Infinite Cyclic Group: Also known as
An infinite cyclic group is also known as a free group on one generator.
From Integers under Addition form Infinite Cyclic Group, the additive group of integers $\struct {\Z, +}$ forms an infinite cyclic group.
Thus the notation $\Z$ is often used for the infinite cyclic group.
This is justified as, from Cyclic Groups of Same Order are Isomorphic, $\Z$ is isomorphic to $\gen a$.