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...
8 α = (д 1 9 2 5 3 4 5 10 3 6 7 86 9 10 2 7 10) 1 4 1 в = (1, 2 3 3 5 4 8 5 2 6 9 7 7 8 4 9 6 10 1 10) 10 8 ү 1 3 2 7 3 9 4 5 1 5 6 7 8 2 9 4 19) 10 1 ө ( 42 2 4 5 4 6 5 2 6 7...
(1 point) Let f be a permutation on the set {1, 2, 3, 4, 5, 6, 7, 8, 9), defined as follows f= 1 2 3 4 5 6 7 8 9 1 2 5 8 3 9 4 6 7 (a) Write the permutation f7 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 answer. (b) Determine the smallest value of k > O such that...
(1) Write the permutation 1 2 3 4 5 6 7 8 9 10 7 5 10 3 8 9 6 2 4 ( 10 1 as a product of disjoint cycles.
(3) (20 points) The following questions pertain to permutations in Sg. (a) Decompose the permutation o= (1 2 3 4 5 6 7 (3 6 4 1 8 25 ) into a product of disjoint cycles. (b) Decompose the permutation t = (1,4, 3) (5,7,6,8) into a product of transpositions. (c) Determine whether o and Tare even or odd permutations. (d) Compute the product ot.
1. Write the permutation o = (6, 1)(4, 2)(1, 2, 3)(5,8)(1, 2) of Sg as a product of independent cycles. Is o an element of Ag? Find the order of o. Find the inverse of o. Justify your answers.
9. Let f be the following permutation in the symmetric group S9, written in two-line notation. 1 2 3 4 5 6 7 8 9 5 9 4 8 2 6 1 3 7 (a) Determine f3121 and explain why your answer is correct. (b) Determine ord(f) (c) Find a permutation p such that p-f 9. Let f be the following permutation in the symmetric group S9, written in two-line notation. 1 2 3 4 5 6 7 8 9...
ASAP (3) (20 points) The following questions pertain to permutations in Sg. (a) Decompose the permutation o = (1 2 3 4 5 6 7 8) into a product of disjoint cycles. 3 6 4 1 8 2 5 (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 productot.
6. Compute the orders of the permutations (2 1 4 6 3), (1 2)(3 4 5) and (1 2)(34). 7. Compute the orders of the following products of non-disjoint cycles: (1 2 3)(2 3 4);(1 2 3)(3 2 4);(1 2 3)(3 4 5). Show your work Ans 6. The orders are 5, 6 and 2 respectively. 7. The orders are 2, 3 and 5.