Find the number of G-orbits in X := {1,2,3, 4, 5, 6, 7, 8, 9, 10}, where G < S10 is the subgroup generated by the cycles (1, 2); (3,4, 5); and (6, 7,8,9).

Q: The elements of the quotient group (/18) are 1- 2- {.-208,-108,008,108,208,.} 3- (0,1,2,3, .8) 4-…

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A: To find Number of  cyclic subgroups does U(15) have

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A: t-test for dependent groups: The paired t-test, also known as the “dependent t-test”, is a…

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A: Topic:- range on number line

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A: We use the Cayley table.

Q: (a) G = Z12 and H = { 0, 2, 4, 6, 8, 10 } (based from the operation table) (b) G = Z; and H = { 1,…

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A: To find: Galois group of x4 + 2x2+ x + 3 over Q. Definition: If there is a field KF such that f…

Q: (a) (Z4, +). (b) (Z5, .). (c) (Z5, +). (d) (Z4, .). (e) (Z6, .).

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Q: Q3:(A) Prove that every group of order 15 is decomposable and normal. (B) Show that (H,.) is a…

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Q: Show that no proper subgroup of S4 contains both (1,2,3, 4) and (1,2).

A: We have to show that no proper subgroup of S4 contains both 1,2,3,4 and 1,2. We know that the…

Q: Prove that a group of class equation 24 = 1+1+4+4+4+4+6 does not have a normal subgroup of order 4.

A: Prove that a group of class equation 24 = 1+1+4+4+4+4+6 does not have a normal subgroup of order 4.

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Q: 1) Prove that G = {a + bv2 \a,b € Q and a, b # 0} is a subgroup of (R – (0},.)

A: Subgroup

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Q: [S,*]= [Z,+] and [S',*']=[Z,∘] where a∘b=a+b-1. Then ?(n)=n+1 is an isomorphism from [Z,+] to [Z,∘]

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Q: Let G and H be groups, and let 0 : G -» H be a {x E G 0(x) = e} is called the kernel of 0 and is…

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A: In group theory, a branch of mathematics, given a group G under a binary operation ∗, a subset H of…

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Q: Are there any other subgroups of order 3 & 2 ? For his vere'll consider all subsets of 3 and 2…

A: We see that S3 is a group of six elements. f is the element in S of order 3. Hence, &lt;f&gt;, &lt;f…

Q: Q1// Let H={2^n: n in Z}. Is H subgroup of Q- * {0}

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Q: Let G = U56 and define two subgroups H₁ and H₂ of G by := H₁ := Calculate H₁ H₂|. {1, 5, 9, 13, 25,…

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Q: Q1/ If (H,*) is collection of subgroups of (G,*) then (U H,*) is subgroup of (G,*)

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Q: What are the eight steps in computing a t-test for dependent groups

A: The paired t is used when the two sample are paired or related samples. When the sample is measured…

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Q: Qi/ If (H,*) is collection of subgroups of (G,*) then (U H,*) is subgroup of (G,*) Q2/ In (Z9, +9)…

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Q: Exercises: Is (H,*) a subgroup of (G,*) each of the following: (1) (Zs. +s), H={0, 6}. Find H. (2)…

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