Exercise · ZW-SYMMETRIC-GROUP-004 · ★☆☆ Basic
If \(\sigma=[2,3,1,4]\) in \(S_4\) (list \([\sigma(1),\ldots,\sigma(4)]\)), what is \(\sigma^{-1}\)?
Choose one option.
Show answer
- B. \([3,1,2,4]\)
Explanation
Since \(\sigma(1)=2\), we need \(\sigma^{-1}(2)=1\); likewise \(\sigma^{-1}(3)=2\), \(\sigma^{-1}(1)=3\) and \(\sigma^{-1}(4)=4\).
Review the concept: Symmetric group
The symmetric group \(S_n\) is the set of bijections \(\sigma\) of \(\{1,\dots,n\}\) onto itself, with composition \(\sigma\tau\) as the operation.
\[(\sigma\tau)(i)=\sigma(\tau(i))\]
More practice problems: symmetric group
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