Group of Order 15 is Cyclic Group/Proof 1

Proof
We have that $15 = 3 \times 5$.

Thus:
 * $15$ is square-free
 * $5 \equiv 2 \pmod 3$
 * $3 \equiv 3 \pmod 5$

The conditions are fulfilled for Condition for Nu Function to be 1.

Thus $\map \nu {15} = 1$ and so all groups of order $15$ are cyclic.