B-Algebra/Examples

Examples of $B$-Algebras

$B$-Algebra Induced by $S_3$

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

$\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}$