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## Related Advanced Math Q&A

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Q: d b belong to a group. If lal = 12. Ibl = 22. and (a) n (b) £fe}, prove that a6 – h11

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

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Q: 4. Which of the groups U(14), Z6, S3 are isomorphic?

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Q: 1. Suppose that an < bn for all n, an → L, and bn → M. Show that L < M.

A: As per our guideline we are supposed to answer only one question.kindly repost other question. The…

Q: Suppose gcd(a, b) = 1. Prove that if r|a and s|b, then gcd(r, s) = 1

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Q: How many subgroups in Z/30Z 4 30 6 CO

A: Here we have group z/30z and find its number of subgroups.

Q: 2. 20 Wnat is the loargest order of an element in Zs Ze O Z 2) Exhibit an element with this arder,

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Q: Suppose chips are randomly drawn from a bag, and each chip is labeled with either 1, 2, 3, 4, 5, 6,…

A: S={1, 2, 3, 4, 5, 6, 7, 8, 9} n(S) = 9 E = odd number = {1,3,5,7,9} n(E) = 5

Q: 1. For every element x in A, there is an element y in B such that (x, y)EF

A: Remark: Let A and B be two non-empty sets. A relation R from A into B is subset of A*B. A function f…

Q: Suppose a e Z. If a² is not divisible by 4, then a is odd.

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Q: . Prove the following: If gcd(a, b) = 1 and ca then gcd(b, c) = 1

A: We will prove the given statement.

Q: Let E = Q(V2,v3,V5). (1) Find 3 distinct non-trivial elements in Aut(E/Q). (2) Denote such three by…

A: Consider the given

Q: Let H x K = { (h,k) |h in H, k in K} such that (h1,k1) + (h2,k2) = (h1 + h2, k1 + k2), for all h1,…

A: here ℤ2=0,1

Q: @ 2 show Hhat fox) = e*-x3+2 2+2 is a %3D Permutation on R.

A: In the give question we have to show that the function f(x)=e-x-x3+2 is a permutation on ℝ.…

Q: 6.4 # 2 Find the matia * ' elative to the basir B' for T A' =

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Q: In Z24 the number of all subgroups is 8 O 6.

A: We are asked to find the subgroup of z24

Q: In the group U (I6) compute, (a) 5.7, and (b) 3

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Q: Let C: z-3 and I – 6dz. ONone of these

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Q: G is Klein's 4-group%3D{e,a,b,c}, H=, then [G:H] is 3 4 O 1 O 2 None of them

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Q: Let d=(1234)(3456)E S, be permutation. a 9. (i) Decidle whe ther d odd. even or Find the ader of d…

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Q: 6. Suppose (a, m) = 1. Prove that for any b, Σ an + b) 1 (т — 1). n<m

A: Given (a,m) = 1 We have to prove that for any b , ∑n≤man+bm = 12(m-1)

Q: 10. Let E = Q(V2, V5). What is the order of the group Gal(E/Q)? What is the order of Gal(O(V10VO)?

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Q: 0:230 → 230 A GROUP HOMOMORPHI KER (o) = {0,5,10,15, 20, 25} %3D o(13)= 6 o"(6) FIND ? now THAT, O

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Q: Let M = {14*: k E Z*} and A = {7k:k E Z*}. Then ACM A=M MC A None of these

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

A: The given group is ℤ8=0,1,2,3,4,5,6,7 with the binary operation defined as ∀ a,b ∈ℤ8a ⊕8 b=a+b mod 8

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

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Q: In the group U (16) compute, (a) 5-7, and (b) 3-1

A: M(16) refers to th e multiplication group of non-negative integers (mod 16) that are less than 16…

Q: 1) In a group G, let a and b be two elements such that a b-ba, o(a)-4 and o(b)-5. Prove that n =…

A: As per our guideline we are supposed to answer only one question you can repost other questions in…

Q: Q3. Prove that if kx = ky (mod m) , then x = y (mod m/d) where d = gcd( m, k).

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Q: 27. If g and h have orders 15 and 16 respectively in a group G, what is the order of (9) n (h)?

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Q: 2. Suppose a, b, and care integers. Prove that if a |band alethen a |b+c and a|b-c.

A: Assume a|b and a|c.

Q: 1. For every element x in A, there is an element y in B such that (x, y) E F.

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Q: (5,00 Puanlar) 2 How many homomorphisms are there from Z12 to Z1s? a) 2 b) 4 C) d) e) Boş bırak

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Q: Please solve this Abstract algebra question.

A: Consider the provided question, (a) Given a = 6, b = 2 So, a + b = 6 + 2 = 8

Q: Show that for n, m e Z+, gcd(2" – 1,2 – 1) = 28cd(n,m) – 1.

A: To prove : gcd(2n-1, 2m-1)=2gcd(n,m)-1where n,m ∈ℤ+

Q: 1. Which of the groups U(14), Z6, S3 are isomorphic?

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Q: Let G = U(15) and N = U,(15).If U(n) = {x E U(n) such that x mod k = 1}, then the factor group G/N…

A: We have to solve given problem:

Q: If a is an element of order n and gcd (p, n) =1.Then show that a^p is also of order n

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Q: Suppose chips are randomly drawn from a bag, and each chip is labeled with either 1, 2, 3, 4, 5, 6,…

A: Given data, 1, 2, 3, 4, 5, 6, 7, 8 or 9 Let E = "choose an odd number" E={1,3,5,7,9} F = "choose a…

Q: Let G = U(15) and N = U3(15) and let Ur (n) = {x € U(n) such that x mod k = 1}. The factor group G/N…

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Q: Let G be a finhte cyclic geupnd a be an clem ent of G of order 8 then the order of G would be O 18…

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Q: Let G = U(15) and N = U,(15).If Ux(n) = {x E U(n) such that x mod k = 1}, then the factor group G/N…

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Q: Let E = Q(√2, √5). What is the order of the group Gal(E/Q)?What is the order of Gal(Q(√10)/Q)?

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Q: 7. Let c t- are both even or both odd. Let that o and(t 0, t be permutations in S. Prove t

A: Every permutation can be written as a product of 2 - cycles.Suppose σ = d1 d2 - - -dsand ζ = B1…

Q: 6.2 Which of the following groups are cyclic? a) Z12×Z, b) Z10×Z85 c) Z4xZ25x Z, d) ZnxZ2 x Z65 -21

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Q: ) Show that Sn is generated by ((1,2),(1,2, 3, n)}. [Hint: Show that as r varies, (1.2,3. ny(1,2)…

A: Please check step 2 for solution

Q: Suppose G is a group and r, be G so that r = b and r = b. Solve for a in terms of b.

A: Given: G is a group, and x,b∈G, so that x3=b5 and x8=b2. Formula used: Basic formula in power and…

Q: 2. Prove that any two non-zero elements a, b in a P.I.D. R have a g.c.d. Further if d e R is a…

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Q: b) Prove, by induction, that for any k >1 and any choice of c1,..., Ck ER and x1,.., X E V, if v =…

A: Given that Sv=v+w:w∈W. b) To prove that Sv=∑i=1kc1Sxi where v=∑i=1kcixi. To prove this by…

Q: Show that if aEG, where G is a group and |a| = n then : %3D a' = a' if and only if n divides. -j

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