Group of Gaussian Integer Units/Cayley Table

Cayley Table for Group of Gaussian Integer Units

The group of Gaussian integer units:

$\struct {U_\C, \times}$

can be described completely by showing its Cayley table:

$\begin{array}{r|rrrr}

\times & 1 & i & -1 & -i \\ \hline 1 & 1 & i & -1 & -i \\ i & i & -1 & -i & 1 \\ -1 & -1 & -i & 1 & i \\ -i & -i & 1 & i & -1 \\ \end{array}$


Sources

  • 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text I$: Algebraic Structures: $\S 6$: Isomorphisms of Algebraic Structures: Example $6.2$
  • 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 34$. Examples of groups: $(6) \ \text{(i)}$
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