a. Find a generator of the group Z33 other than [1]: is another generator of the cyclic group <[1] >= Z33. b. Find the order of the subgroup <[20] > of the group Z26: |<[20] >| =

Q: Let G = Z8 x Z6, and consider the subgroups H = {(0, 0), (4, 0), (0, 3), (4,3)} and K = ((2, 2)).…

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Q: Imagine  Z9* a cyclic group. What is order of an element a=2 and show the elements? Show all your…

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Q: Let G be a cyclic group of order 135. The number of generators of G is The number of elements of…

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Q: Find the cyclic subgroup of S6 generated by the element (123)(456)

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Q: Consider the factor group G = R* /Q*. Determine which of the following elements in G are equal. 1Qx,…

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Q: 19. Prove that the group (Z/11Z)* is cyclic, and find a generator.

A: We have to prove that the group (Z/11Z)* is cyclic, and find a generator.

Q: . Consider the group (Z30, +). (a) Find the orders of the elements 3, 5, 6, 7,8, 18, 19, 24 and 25.…

A: The order of an element is n , when n is the least such that, n.a=0 3.10 = 0 and 19 the least , so…

Q: Calculate the cyclic subgroup (15) < (Z24, +21)

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Q: Let G be a group. Assume a and b are elements of G and set H₁ = and H₂ =. Assume |H₁| = 21 and |H₂|…

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Q: Determine the group Z42/ and find a group that it is isomorphic to it. Generalize your observation.

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Q: The subgroup 5Z = {5t |t e Z} is a normal subgroup of the additive group Z. Find th order of the…

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Q: (a) Let G = {e, a, . .. , aº | a10 = e} be the cyclic group of order 10. For which m, is G = (am)?…

A: As per our guideline we are supposed to answer only first asked  question. Kindly repost other…

Q: Find the order of the factor group U(16)/(9)where U(16)={1,3,5,7,9,11,13,15} with operation…

A: Since , we have to find order of the factor group U(16)/&lt;9&gt; Concept: Order of factor group…

Q: this question is from a linear algebra course: Given the plane V with the equation n · x = b, where…

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Q: The alternating group A5 has 5 conjugacy classes, of sizes 1, 12, 12, 15, 20. Use this information…

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Q: 10. Let G = Z/36Z. (a) Find the order of every element of the group G. (b) Find all generators of G.

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Q: D Question 2 Let (an) be the sequence from the previous question. To show by induction that an 2" +3…

A: we need to prove by induction an=2n+3 for all natural numbers n  step 1 for n=1  a1=21+3=2+3

Q: express Z10 as a product of Z5 x Z2 , verify that both groups are isomorphic.

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Q: Evaluate the following integral (1 – e *)dx using a composite (Number of segments, n= 6) application…

A: Use Simpsons 3/8 rule:…

Q: (6) Let (G, *) be a group and a € G. Prove that the order of a is equal to the order of a-1. Prove…

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Q: Show that x is not a generator of the cyclic group (Z3[x]/&lt;x3 + 2x + 2&gt;). Find one such…

A: The given cyclic group is: Z3x/x3+2x+2*. We have to show that x is not the generator of the given…

Q: Find all generators of the subgroup of Z/60Z with order 12.

A: Generators of the group

Q: Use the three Sylow Theorems to prove that no group of order 45 is simple.

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