Struct/The group with three elements.

=Definition=

There is a unique group, up to isomorphism, with three elements. One example is the group $(\ZZ / 3 \ZZ, +)$ of residues, mod $3$, displayed below.

=Properties=


 * The group $\ZZ / 3 \ZZ$ is an exemplifies::Def/Abelian group.
 * It is a cyclic group, generated by $\bar 1$.
 * Since $3$ is a prime number, every group with $3$ elements is isomorphic to $\ZZ / 3 \ZZ$.