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QUIZ 3 (20 MIN, OPEN BOOK)

MATH 3175 GROUP THEORY

(Each problem is worth 10 points.)

(1) Consider the permutations  and  in S5.

(a) What is ?

(b) What is τσ?

(c) What is στ?

(2) Let

(a) Write σ as a product of disjoint cycles.

σ = (1, 3, 5, 9, 11, 2)(4, 10, 8, 7)

(there are other correct answers

(b) What is the order of σ?

[6, 4] = 12.

(c) Write the permutation σ = (1, 5, 2, 7)(3, 4, 6) ∈ S7 as a product of transpositions.

(1, 5)(5, 2)(2, 7)(3, 4)(4, 6)

(but there are other correct answers)