Exercise 1.3.20 (Set of generators and relations for $S_3$)

Question

Find a set of generators and relations for $S_3$.

Richard Ganaye · Accepted Answer

\begin{proof} 
Since $S_3 \simeq D_6$, where $r \mapsto (1\ 2\ 3) = \sigma$ and $s \mapsto (1\ 2) = 	au$, then $S_3$ and $D_6$ have the same set of generators and relations:

$$S_3 \simeq \langle \sigma, 	au\mid \sigma^3 = 	au^2 = e,\ 	au \sigma = \sigma^2 	au angle.$$

\end{proof}

Exercise 1.3.20 (Set of generators and relations for $S_3$)

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Exercise 1.3.20 (Set of generators and relations for $S_3$)

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