Struct/The cyclic group with six elements

=Definition=

There is a unique cyclic group, up to isomorphism, with six elements. One example is the group $(\ZZ / 6 \ZZ, +)$ of residues, mod $6$, displayed below.

=Properties=


 * The group $\ZZ / 6 \ZZ$ is an abelian group.
 * It is a cyclic group, generated by $\bar 1$.
 * Every abelian group of order $6$ is isomorphic to $\ZZ / 6 \ZZ$.