Exercise · ZW-SYMMETRIC-GROUP-001 · ★☆☆ Basic
How many elements does \(S_4\) have?
Choose one option.
Show answer
- C. \(24\)
Explanation
Each permutation of four elements comes from choosing distinct images: \(4\cdot3\cdot2\cdot1=24\).
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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- ZW-SYMMETRIC-GROUP-005 What is the smallest n for which S_n is not abelian?
- ZW-SYMMETRIC-GROUP-006 How many permutations σ∈ S_5 satisfy σ(1)=1?
- ZW-SYMMETRIC-GROUP-007 Which statement about S_n is true?
- ZW-SYMMETRIC-GROUP-008 For which n does S_n have exactly 120 elements?
- ZW-SYMMETRIC-GROUP-009 In S_4 let σ=[2,1,3,4] and τ=[1,3,2,4]. What is (στ)(2)?