Automorphism Group/Examples/Cyclic Group C3

Example of Automorphism Group
Consider the cyclic group $C_3$, which can be presented as its Cayley table:

The automorphism group of $C_3$ is given by:


 * $\Aut {C_3} = \set {\phi, \theta}$

where $\phi$ and $\theta$ are defined as:

The Cayley table of $\Aut {C_3}$ is then:


 * $\begin{array}{r|rr}

& \phi  & \theta \\ \hline \phi  & \phi   & \theta \\ \theta & \theta & \phi \\ \end{array}$