Let A = {1,2,3,4,5,6} and p1 = (4,2,5) and p2 = (2,6,1) be permutations of A. Compute p,-1 o p2¬1 and write as a product cycle.

Q: Let σ denote the permutation � 1 2 3 4 5 6 7 8 9 3 8 5 6 7 4 9 2 1� in the symmetric group S9 on the…

A: Given a  permutaion  in the symmetric group S9on the set {1,2,3,4,5,6,7,8,9}1 2 3 4 5 6 7 8 93 8 5 6…

Q: Let A = {a, b, c, d, e, f}. If the permutations P1=(b, a, e, c)  and P2=[a,b,c,d,e,f f,a,c,e,b,d]…

A:

Q: 14. Let A = {1,2,3,4,5,6} and p₁ = (4,2,5) and p₂ = (2,6,1) be permutations of A. Compute p₂¹P₁-1…

A:

Q: Express each permutation as a product of disjoint cycles and find the orbits of each permutation

A: Given: 1234535241

Q: (12 3 4) o (2 3 5 4 6) o (3 4 5 6) can be expressed as product of following disjoint cycles Select…

A:

Q: R the generated of z

A:

Q: Q/ How many non-trivial subgroups in s, ? a) 2 b) 3 c) 4

A: S3 is the set of permutations on the set {1, 2, 3}S3={e, (1 2), (1 3), (2 3), (1 2 3), (1 3 2) }The…

Q: If H and K are subgroups of G, |H|- 16 and K-28 then a possible value of HNK| is 16

A:

Q: 4. The permutations (e, a, B, v) form a group. If e = (1)(2)(3)(4)(5)(6), a = (1)(2)(35)(46), B=…

A:

Q: Determine a series of transformations that would map Figure M onto Figure N. 12 Figure N 11 10 8. 7.…

A: The solution is given in step 2.

Q: Given a=(1 2 3)(4 5) and B= (1 2 5 4 3). Express (aß) as a product of transpositions(2 -cycles). Is…

A: Given α = (1 2 3)(4 5)  and  β = (1 2 5 4 3)

Q: Consider the product of cycles (1 2)(4 7 8)(2 1)(7 2 8 1 5) that are permutations of {1, 2, 3, 4, 5,…

A:

Q: Question 8. Given the permutations 1 2 3 4 1 2 3 4 5 6 and B = 4 a = 2 6 3 1 1 4 (a) Compute B o a .…

A:

Q: In the group S6, consider the elements 1 2 3 4 5 6 4 3 6 5 1 2 1 2 3 4 56 35 4 2 6 1 a = and B = (a)…

A:

Q: Let 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 and B= 2 3 4 5 1 7 8 6 13 8 7 6 5 2 4 Write a, B, and aß as a.…

A:

Q: ] Given the permutations 1 2 3 2 6 3 5 :) 1 2 3 5 3 1 6 4 2 4 6. 4 6. and B = 4 1 (a) Compute B o a.…

A: The objective is to solve the above question.

Q: 25) 26) (1 2 3 4 5 Let a = 2 3 4 5 6 7 8 1 7 8 6 Compute ßa. (1 2 3 4 A. 5 6 7 8 7 8 8) 2 3 4 5 1 2…

A:

Q: If H and K are subgroups of G, |H|= 18 and |K|=30 then a possible value of |HNK| is

A: It s given that H and K are subgroups of G, H=18 and K=30. Since H, K are subgroups, H∩K≤H  and…

Q: (12 3 4) o (2 3 5 4 6) o (3 4 5 6) can be expressed as product of following disjoint cycles Select…

A: To express in disjoint cycles start from right and then go through left to right.

Q: Q/ How many non-trivial subgroups in s3 ? a) 2 b) 3 c) 4

A: We know that S3 = (1) , (1,2) , (1,3) , (2,3) , (1,2,3) , (1,2,3) Thus the subgroups of S3 are given…

Q: In general, if (12 · · · k) is a cycle of length k and o is any permutation then o(12 ·.· k)o -1 =…

A: Given: T=(12.....k)

Q: Find groups that contain elements a and b such that |a|=|b|= 2 and a. |ab| =3, b. |ab| =4, c. |ab|=…

A: Given : |a|=|b|= 2 To find:  |ab| = ?

Q: Suppose that {an} is defined recursively by:   an = (an−1)2 − 1  and that a0 = 2. Find a2 and a3 .

A: Given  an=(an-1)2-1 ao=2

Q: If H and K are subgroups of G, |H|= 16 and |K|=28 then a possible value of |HNK| is * 4 O 16

A:

Q: Express each permutation as a product of disjoint cycles and find the orbits of each permutation…

A: To express the permutation 1, 4, 8, 71, 9, 6, 51, 5, 3, 2, 9 as a product of disjoint cycles…

Q: Express each permutation as a product of disjoint cycles and find the orbits of each permutation

A: Given that, Let p = 1  2  3  4  5   6  73  4  5  6  1   2  7  be a permutation Two cycles are said…

Q: Enter the smallest subgroup of M₂ (R)* containing the matrix -5 -3 7 4 as a set

A: Given: -5-374∈M2ℝ* To find: Smallest subgroup of M2ℝ* containing given element.

Q: Q/ How many non-trivial subgroups in s3 a) 2 b) 3 c) 4 d) 5

A: The set S3 is given by  S3=e, 12, 13, 123, 132 The subgroups of S3 are e, e, 12, e, 13, e, 23, e,…

Q: Example: H.W In the group (Z6,+6) find the order of each element in

A: Explanation of the solution is given below....

Q: In the group Z8 compute, (a) 6+7, and (b) 2-1.

A:

Q: which of the following group are cycle ?(a) U(35) (b)U5(40)

A: It is required to check which of the given group are cyclic. (a) U(35) (b)U5(40)

Q: et n ≥ 3. (a) Find the number of permutations w ∈ Sn such that 1, 2, 3 belong to three distinct…

A: denotes symmetric group.

Q: If o is a cycle of length n, then a' is also a cycle if and only if... 50) Show that S is generated…

A:

Q: ng to a group. If |a| = 12, |6| = 22, and (a) N (b) # {e}, prove that a® = b'1.

A:

Q: (Z., +6) is a subgroup of (Zg, +8)

A:

Q: List all generators of (Z10, +10)

A:

Q: Question 2 (Cyc Given positive integers a1, a2, ...,ak with a1 + a2 +...+ ag = n, how many…

A: Given that there are a1,a2,...,ak positive integers. Also a1+a2+...+ak=n. Without loss of generality…

Q: Express each permutation as a product of disjoint cycles and find the orbits of each permutation

A: In this permutation  1→12→3→24→5→4

Q: [1 2 3 4 5 5 2 3 4 1 [1 2 3 4 5] 1 5 4 3 2 1. Let o = and T = be permutations in S6. (a) (2 points)…

A:

Q: Let 1.2,3/45,6,77) Flod the cycle decomposi: of Y

A:

Q: (c) Define a permuta (d) Express the product of the cycles (1,2)(4,7,8) (2, 1) (7.2.8.1.5), as a…

A:

Q: If o is a k-cycle then the order of o is k. On the otherhand, if 7 is a product of disjoint cycles…

A: a) since this is a four cycle , then order is 4  b) order is lcm(3,4) = 12 c) order is lcm(4,2,3)…

Q: Express each permutation as a product of disjoint cycles and find the orbits of each permutation

A: a)1234523415b)1234513542

Q: List all elements of U(10) and give a multiplication table for the group U(10)

A: Given  that, The group U(10). We have to find the all elements in U(10) and multiplication table for…

Q: Label eachof the following statement/s as either true or false. The mutually disjoint cycles of a…

A: Solution: Consider the given statement is: The mutually disjoint cycles of a permutation are the…

Q: .

A: To prove : The two cycles (a1,a2,...ak), (b1,b2,...bm) are disjoint cycles. If the pair of cycles ↵…

Q: need help with cyclic groups plz, thanks

A: Given groups are,

Q: Suppose a permutation s swaps the first two elements of {1, 2, ..., n}. A permutation r rotates the…

A: Given set is 1,2,...,n. Now, rm  make the circular shift of m number of the elements and then the…

Q: 1 23 4 5 6 7 245 137 6 1 2 3 4 5 6 7 and B= 2 67 4 15 %3D Given a = a)(8) Express Ba as a cycle or…

A:

Q: Find all generators of Z6, Z8, and Z20.

A: To find generators of ℤ6, ℤ8, and ℤ20