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Struct/The cyclic group with six elements
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Title: The group with three elements.
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.
| $+$ | $\bar 0$ | $\bar 1$ | $\bar 2$ | $\bar 3$ | $\bar 4$ | $\bar 5$ |
|---|---|---|---|---|---|---|
| $\bar 0$ | $\bar 0$ | $\bar 1$ | $\bar 2$ | $\bar 3$ | $\bar 4$ | $\bar 5$ |
| $\bar 1$ | $\bar 1$ | $\bar 2$ | $\bar 3$ | $\bar 4$ | $\bar 5$ | $\bar 0$ |
| $\bar 2$ | $\bar 2$ | $\bar 3$ | $\bar 4$ | $\bar 5$ | $\bar 0$ | $\bar 1$ |
| $\bar 3$ | $\bar 3$ | $\bar 4$ | $\bar 5$ | $\bar 0$ | $\bar 1$ | $\bar 2$ |
| $\bar 4$ | $\bar 4$ | $\bar 5$ | $\bar 0$ | $\bar 1$ | $\bar 2$ | $\bar 3$ |
| $\bar 5$ | $\bar 5$ | $\bar 0$ | $\bar 1$ | $\bar 2$ | $\bar 3$ | $\bar 4$ |
