Monthly Archives: June 2017

a group

SL_2(Z_3)

Group SL_2(\Bbb Z_3):

a=\left(\begin{array}{cc}0&1\\2&0\end{array}\right) , b=\left(\begin{array}{cc}0&1\\2&1\end{array}\right) , ba^3b=\left(\begin{array}{cc}0&1\\2&2\end{array}\right)

a^3=\left(\begin{array}{cc}0&2\\1&0\end{array}\right) , bab=\left(\begin{array}{cc}0&2\\ 1&1\end{array}\right) , a^2b=\left(\begin{array}{cc}0&2\\1&2\end{array}\right)

e=\left(\begin{array}{cc}1&0\\ 0&1\end{array}\right) , a^2ba=\left(\begin{array}{cc}1&0\\ 1&1\end{array}\right) , (ba)^2=\left(\begin{array}{cc}1&0\\2&1\end{array}\right)

(ab)^2=\left(\begin{array}{cc}1&1\\0&1\end{array}\right) , b^2ab=\left(\begin{array}{cc}1&1\\ 1&2\end{array}\right) , a^3ba=\left(\begin{array}{cc}1&1\\2&0\end{array}\right)

a^3b=\left(\begin{array}{cc}1&2\\0&1\end{array}\right) , a^2b^2=\left(\begin{array}{cc}1&2 \\1&0\end{array}\right) , bab^2=\left(\begin{array}{cc}1&2\\2&2\end{array}\right)

a^2=\left(\begin{array}{cc}2&0\\ 0&2\end{array}\right) , ab^2=\left(\begin{array}{cc}2&0\\ 1&2\end{array}\right) , ba=\left(\begin{array}{cc}2&0\\ 2&2\end{array}\right)

ab=\left(\begin{array}{cc}2&1\\ 0&2\end{array}\right) , b^2aba=\left(\begin{array}{cc}2&1\\ 1&1\end{array}\right) , b^2=\left(\begin{array}{cc}2&1\\2&0\end{array}\right)

b^2a=\left(\begin{array}{cc}2&2\\0&2\end{array}\right) , aba=\left(\begin{array}{cc}2&2\\1&0\end{array}\right) , abab^2=\left(\begin{array}{cc}2&2\\2&1\end{array}\right)

Advertisements