The permutation $$ g=\left(\begin{array}{llllllll}1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \ 8 & 5 & 6 & 3 & 2 & 7 & 4 & 1\end{array} ight) $$ from the symmetric group $$ S_{8} $$ is even. True of false?

Question

The permutation $$ g=\left(\begin{array}{llllllll}1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \ 8 & 5 & 6 & 3 & 2 & 7 & 4 & 1\end{array}ight) $$ from the symmetric group $$ S_{8} $$ is even. True of false?

John Patel · Accepted Answer

The permutation $$ g $$ is odd, so the statement is false.

The permutation \( g=\left(\begin{array}{llllllll}1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ 8 & 5 & 6 & 3 & 2 & 7 & 4 & 1\end{array}\right) \) from the symmetric group \( S_{8} \) is even. True of false?

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The permutation \( g=\left(\begin{array}{llllllll}1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ 8 & 5 & 6 & 3 & 2 & 7 & 4 & 1\end{array}\right) \) from the symmetric group \( S_{8} \) is even. True of false?

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