Category:Cyclic Group of Order 8 is not isomorphic to Group of Units of Integers Modulo n

This category contains pages concerning Cyclic Group of Order 8 is not isomorphic to Group of Units of Integers Modulo n:

Let $n \in \Z_{\ge 0}$ be an integer.

Let $\struct {\Z / n \Z, +, \cdot}$ be the ring of integers modulo $n$.

Let $U = \struct {\paren {\Z / n \Z}^\times, \cdot}$ denote the group of units of $\struct {\Z / n \Z, +, \cdot}$.

Let $C_8$ denote the cyclic group of order $8$

Then:

$U$ and $C_8$ are not isomorphic.