Modulo Addition/Cayley Table/Modulo 3

Cayley Table for Addition Modulo $3$

The additive group of integers modulo $3$ can be described by showing its Cayley table:

$\begin {array} {r|rrr} \struct {\Z_3, +_3} & \eqclass 0 3 & \eqclass 1 3 & \eqclass 2 3 \\ \hline \eqclass 0 3 & \eqclass 0 3 & \eqclass 1 3 & \eqclass 2 3 \\ \eqclass 1 3 & \eqclass 1 3 & \eqclass 2 3 & \eqclass 0 0 \\ \eqclass 2 3 & \eqclass 2 3 & \eqclass 0 3 & \eqclass 1 3 \\ \end {array}$

It can also be presented:

$\begin {array} {r|rrr} +_3 & 0 & 1 & 2 \\ \hline 0 & 0 & 1 & 2 \\ 1 & 1 & 2 & 0 \\ 2 & 2 & 0 & 1 \\ \end {array}$

Sources

• 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 6.7$. Quotient groups: Example $126$
• 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Chapter $\text{II}$: Groups: A Little Number Theory
• 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $2$: Maps and relations on sets: Example $2.33$