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Abstract Algebra

Exercise 1.3.7 (Cycle decomposition of the elements of order 2 in $S_4$)

Write out the cycle decomposition of each element of order 2 in S 4 .

Answers

Proof. We keep only the elements of order 2 in the array of Exercise 4(b)

σ | σ | ( 1 2 ) 2 ( 1 3 ) ( 2 4 ) 2 ( 1 4 ) ( 2 3 ) 2 ( 1 3 ) 2 ( 3 4 ) 2 ( 2 4 ) 2 ( 1 4 ) 2 ( 2 3 ) 2 ( 1 2 ) ( 3 4 ) 2

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2025-09-12 10:37
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