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.
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...
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...
(3) (20 points) The following questions pertain to permutations in Sg. (a) Decompose the permutation o (1 2 3 4 5 6 7 %) into a product of disjoint cycles. (3 6 4 1 8 2 5 7 (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.
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.
(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.
Let wE S7 be a permutation which rearranges 7 objects as follows, showing the result on the lower line 2 3 4 6 7 5 5 4 2 7 6 1 3 a) Express was a product of disjoint cycles representing how each object moves Is w an even permutation, or an odd permutation? What is its order? products of disjoint cycles b) Calculate w3, w5 and w' 2 as c) Does there exist T E S7 for which T-lwr...
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. 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.
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