Question First, fattorize each of the following permutations as product of disjoint cycles, then secondly factorize...
The following questions pertain to permutations in (a) Decompose the permutation into a product of disjoint cycles. (b) Decompose the permutation into a product of transpositions. (c) Determine whether σ and τ are even or odd permutations. (d) Compute the product σ τ.
2. Write each of the following permutations in Sg as a product of disjoint cycles: (1245) (245) (321) = (12)(123)(3214)-! = (1245)2 = (1238) (457)(68) = (12)(23)(34)(45) = (15)(14)(13)(12) =
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.
(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.
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.
Exercises xpress each permutation as a product of disjoint cycles and find the orbits of each permutation 331 1 1 2 3 4 5 b.
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...
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.
2. s each permutation as a product of disjoint cycles and find the orbits of each permutation. a. (1, 9,2,3X1,9,6, 5)X1,4, 8,7) b.21,2,9x3,4)(5, 6, 7,8,9)%4,9) d. (1, 4,2, 3, 5X1, 3, 4, 5) f(1,9,2,41,7,6,5, 9(1.2,3,8) h. (4,9, 6,7, 8)(2, 6.41.8 73 (2,3,71, 2x3,5,7,6,4X1,4)