I'm really struggling trying to prove that the Klein group $V_4$ is isomorphic to $C_2\times C_2$. Can someone please help me?
2026-04-07 17:16:06.1775582166
Prove that the Klein group $V_4$ is isomorphic to $C_2\times C_2$
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Hint:
Table for $V_4$ $$\begin{array}{|c|c|c|c|c|} \hline *& e & a & b & c \\ \hline e & e&a&b&c\\ \hline a & a& e&c&b\\ \hline b & b& c&e&a\\ \hline c & c& b& a& e \\ \hline \end{array}$$
Table for $C_2\times C_2$
$$\begin{array}{|c|c|c|c|c|} \hline +& (0,0) & (0,1) & (1,0) & (1,1) \\ \hline (0,0) &(0,0)&(0,1)&(1,0)&(1,1)\\ \hline (0,1) & (0,1)&(0,0)&(1,1)&(1,0)\\ \hline (1,0) &(1,0)&(1,1)&(0,0)&(0,1)\\ \hline (1,1) & (1,1)&(1,0)&(0,1)&(0,0) \\ \hline \end{array}$$