Solve for 1 Consider the following permutations f, g, and h in S6 - (1 2...
abstract-algebra
Problem 10.2. Consider the following permutations f and g in the permutation group 56: f:145, 241, 366,44 3,5 H 2,6 H4; g=(1 6 5)( 24). (1) Write f as a product of disjoint cycles. (2) Find o(g). (3) Write fg as a product of disjoint cycles. (4) Write gf as a product of disjoint cycles. (5) Write gfg as a product of disjoint cycles. Hint. All should be straightforward. Be careful though.
Q= II. Permutations. Consider the following permutations in Sg: 1 2 3 4 5 6 7 8 9 3 1 4 5 9 2 6 8 7 2 7 1 8 4 5 9 3 6 1. Express a and B as products of disjoint cycles. 2. Compute a-108-1 3. Find ord(a) and ord(B). 4. Express a and B as products of transpositions.
(1 point) Let f and g be permutations on the set {1, 2, 3, 4, 5, 6, 7}, defined as follows (1 2 3 4 5 6 7 JE (3 1 6 5 7 2 4) f = (1 800 2 5 3 4 4 7 5 3 6 2 7 6) Write each of the following permutations as a product of disjoint cycles, separated by commas (e.g. (1,2), (3,4,5), ... ). Do not include 1-cycles (e.g. (2)) in your...
By a, b, f, r, the following permutations of the set
{1,2,3,4,5,6} are given.
a) Determine the unknown permutations g and h if the equations
for g ◦ h = r and h◦a = b apply.
b) Find (f ◦g◦h)2 = (f ◦g◦h) ◦ (f ◦g◦h).
142635 b=(425163 r=(314562) 6 4 3 21' = 521),
142635 b=(425163 r=(314562) 6 4 3 21' = 521),
4. Determine the disorder of the permutation (1 3 5 6 2) in S6. Write (1 3 5 6 2) as a product of as few as possible simple transpositions. (Simple transpositions are permutations which swap objects in adjacent positions only.) Justify why your product is as short as possible.
4. Determine the disorder of the permutation (1 3 5 6 2) in S6. Write (1 3 5 6 2) as a product of as few as possible simple transpositions....
4. Determine the disorder of the permutation (1 3 5 6 2) in S6. Write (1 3 5 6 2) as a product of as few as possible simple transpositions. (Simple transpositions are permutations which swap objects in adjacent positions only.) Justify why your product is as short as possible.
4. Determine the disorder of the permutation (1 3 5 6 2) in S6. Write (1 3 5 6 2) as a product of as few as possible simple transpositions....
Question 9 (6 points) (2,4, 3) and g (1, 5, 2) are permutations defined on S -(1, 2, 3, 4, 5), What is a) (fog)(4) [What is the result of applying fo g to 4] (gof)(5) [What is the result of applying g e f to 5] b)
Consider the following reaction at 298K. Sn2+ (aq) + H2(g) -Sn (8) + 2 H+ (aq) Which of the following statements are correct? Choose all that apply. OK>1 n= 4 mol electrons delta Gº> The reaction is reactant-favored. E cell > 0 Sited
The following questions pertain to permutations in S8 (a) Decompose the permutation (1 2 3 4 5 6 7 %) into a product of disjoint 13 6 4 1 8 2 5 7 cycles. = (b) Decompose the permutation T= (1,4, 3) (5,7,6,8) into a product of transpositions. (c) Determine whether o and T are even or odd permutations. (d) Compute the product OT.
a = 14. Consider the permutations (13)(24)(56) and B = (1 4)(26)(35) expressed in cycle notation. How many permutations y of {1,2,3,4,5,6} exist with the property B = y lay where we compose from left to right? (b) 48 (c) 6 (d) 24 (e) 3 (a) 8 1 15. You are given that {a,b,c} = {1,2,3} and, from the 8-puzzle 2 3 4 5 6 7 8 the following configuration has been reached by moving squares in and out of...