Multiplicative Group of Reduced Residues Modulo 7/Cayley Table
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Cayley Table for Multiplicative Group of Reduced Residues Modulo 7
The multiplicative group of reduced residues modulo $7$:
- $\Z'_7 = \set {\eqclass 1 7, \eqclass 2 7, \eqclass 3 7, \eqclass 4 7}, \eqclass 5 7, \eqclass 6 7$
can be described completely by showing its Cayley table:
- $\begin{array}{r|rrrr} \times_5 & \eqclass 1 7 & \eqclass 2 7 & \eqclass 3 7 & \eqclass 4 7 & \eqclass 5 7 & \eqclass 6 7 \\ \hline \eqclass 1 7 & \eqclass 1 7 & \eqclass 2 7 & \eqclass 3 7 & \eqclass 4 7 & \eqclass 5 7 & \eqclass 6 7 \\ \eqclass 2 7 & \eqclass 2 7 & \eqclass 4 7 & \eqclass 6 7 & \eqclass 1 7 & \eqclass 3 7 & \eqclass 5 7 \\ \eqclass 3 7 & \eqclass 3 7 & \eqclass 6 7 & \eqclass 2 7 & \eqclass 5 7 & \eqclass 1 7 & \eqclass 4 7 \\ \eqclass 4 7 & \eqclass 4 7 & \eqclass 1 7 & \eqclass 5 7 & \eqclass 2 7 & \eqclass 6 7 & \eqclass 3 7 \\ \eqclass 5 7 & \eqclass 5 7 & \eqclass 3 7 & \eqclass 1 7 & \eqclass 6 7 & \eqclass 4 7 & \eqclass 2 7 \\ \eqclass 6 7 & \eqclass 6 7 & \eqclass 5 7 & \eqclass 4 7 & \eqclass 3 7 & \eqclass 2 7 & \eqclass 1 7 \\ \end{array}$