1. Write the permutation o = (6, 1)(4, 2)(1, 2, 3)(5,8)(1, 2) of Sg as a...
(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.
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.
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....
(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.
(1 2 3 4 5 6 7 8 2. Let o = 4. LALO (5 4 76 2 18 3) a. Write o as a product of disjoint cycles. b. Compute ord(o) = the order of o in Sg.
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...
Problem 10.3. Consider the following permutation f in the permutation group Sz: f:1-3, 2 H+ 6, 3 - 3, 4 +5,5 2),6 2,7 H 1. Furthermore, it is known that f is odd. (1) Determine f by writing f as a product of disjoint cycles. (2) Determine of). (3) Compute f17 by writing f17 as a product of disjoint cycles. (4) Write f as a product of transpositions. Hint. The fact that f e Sy should narrow it down to...
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.