(c) In this part of the question we consider U25 as a group under multiplication. Let a E Z. Suppose that 5 a. (1) Suppose that [al0]25 [1]25 and [a*]25 # [1]25. Prove that (la)25) = U25. %3D (ii) Show that ((2]25) = U25. (ii) Suppose that ([a]25) = U25. Show that ([a']25) = U25. %3D %3D

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A: please see the next step for solution

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Q: 9. Describe the group of the polynomial (x* – 1) e Q[x] over Q.

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Q: 12. Describe the group of the polynomial (x* – 5x? + 6) € Q[x] o over Q.

A: please see the next step for solution

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Q: 1. 3 in U(11), the group of units modulo 11.

A: As per the guidelines we can answer the first question since u have posted multiple questions.

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Q: (a) Make addition and multiplication tables for Z/3Z.

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

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A: Please find attachment

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A: Given: Group D4=a,b=e=1,a,a2,a3,b,ab,a2b,a3b and a=1 2 3 4, b= 2, 4 To find : The value of…

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A: We know, U(n) is a group under multiplication modulo n which contains those elements who are…

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A: To determine : Whether the given statements are true or false and justify the answers.

Q: Show that cl(a) = {a} if and only if a ∈Z(G).

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A: Good question. Have answered all the details in step 2.

Q: Let a = (17 3)(5 9 4 2) and B = (2 3)(7 4)(5 1 8) be elements of S10. Then, a'ß-1 is O (1 4)( 2758 9…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: A, B, C are coplanar.So

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A: Result: Let G, * be a group and H is a subset. The subset H is said to be subgroup, if for every a,…

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A: according to our guidelines we can answer only three subparts, or first question and rest can be…

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