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)