B-Algebra/Examples/S3

Example of $B$-Algebras

This is a $B$-algebra for the finite set $\set {0, 1, 2, 3, 4, 5}$:

$\quad \begin{array}{c|cccccc} & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline 0 & 0 & 2 & 1 & 3 & 4 & 5 \\ 1 & 1 & 0 & 2 & 4 & 5 & 3 \\ 2 & 2 & 1 & 0 & 5 & 3 & 4 \\ 3 & 3 & 4 & 5 & 0 & 2 & 1 \\ 4 & 4 & 5 & 3 & 1 & 0 & 2 \\ 5 & 5 & 3 & 4 & 2 & 1 & 0 \\ \end{array}$

Proof

This theorem requires a proof. In particular: Demonstrate that it is the $B$-algebra induced by $S_3$ You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 2002: J. Neggers and Hee Sik Kim: On B-Algebras (Matematički Vesnik Vol. 54: pp. 21 – 29)