Question

Question: Find the left regular representation of each group (that is, express each group as a permutation group as in the proof of Theorem 7.21):

(a)${\mathrm{\mathbb{Z}}}_3$

Short answer

Answer

The left representation of

$$\begin{gathered} {\mathrm{\mathbb{Z}}}_{4}isA=\{f_{0,}{f}_1,f_2\}where,f_0=\left(\begin{array}{ccc}0& 1& 2\\ 0& 1& 2\end{array}\right),f_1=\left(\begin{array}{ccc}0& 1& 2\\ 1& 2& 0\end{array}\right) \\ {f}_2=\left(\begin{array}{ccc}0& 1& 2\\ 2& 0& 1\end{array}\right) \end{gathered}$$

Step-by-step solution

a

s