Finite Group Z8

$\begin{figure}\begin{center}\BoxedEPSF{Z8.epsf}\end{center}\end{figure}$

One of the three Abelian groups of the five groups total of Order 8. An example is the residue classes modulo 17 which Quadratic Residues, i.e., $\{1, 2, 4, 8, 9, 13, 15, 16\}$ under multiplication modulo 17. The elements satisfy ${A_i}^8=1$ , four of them satisfy ${A_i}^4=1$ , and two satisfy ${A_i}^2=1$ . The Cycle Graph is shown above.