Q= II. Permutations. Consider the following permutations in Sg: 1 2 3 4 5 6 7...
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.
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.
(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...
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.
This is all about abstract algebra of permutation group. 3. Consider the following permutations in S 6 5 3 489721)' 18 73 2 6 4 59 (a) Express σ and τ as a product of disjoint cycles. (b) Compute the order of σ and of τ (explaining your calculation). (c) Compute Tơ and στ. (d) Compute sign(a) and sign(T) (explaining your calculation) e) Consider the set Prove that S is a subgroup of the alternating group Ag (f) Prove that...
(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...
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.
(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.