Exercise · ZW-SYMMETRIC-GROUP-009 · ★★☆ Intermediate
In \(S_4\) let \(\sigma=[2,1,3,4]\) and \(\tau=[1,3,2,4]\). What is \((\sigma\tau)(2)\)?
Choose one option.
Show answer
- A. \(3\)
Explanation
Apply \(\tau\) first: \(\tau(2)=3\) and then \(\sigma(3)=3\). The value \(1\) comes from applying the factors in the opposite order, \(\tau\sigma(2)\).
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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