5. List the left and right cosets of the subgroups in each of the following. a. (8) in Z24 C. 3Z in Z b. (3) in U(8) d. A4 in S4

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A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Find a subgroup of S4 which contains six elements. How many subgroups of order six are there in S4?

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Q: 11. Find the cyclic subgroup of D4 generated by µp². What is the order of this subgroup?

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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: 6. Find all of the subgroups in A4. What is the o

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Q: Let H be the subgroup of S4 given by H = {e, (1 2), (1 4), (2 4), (1 2 4), (1 4 2)}. (a) What is the…

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Q: 10. If 4,42..a, is an element in a group, what is (4,az..a,) = ?

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Q: 1. Z30 2. U(14)

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Q: 6.2 Which of the following groups are cyclic? a) Z12×Z, b) Z10x Zgs c) Z4xZ2sx Z, d) Z22XZ21 xZ6s

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Q: 34. Suppose a and b are group elements such that |a| = 2, b ‡ e, and aba = b². Determine [b].

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Q: 8. Is Zg isomorphic to D4? What about Z4 and D4? Can you find a subgroup of D4 isomorphic to Z4?

A: Now we have to answer the above question .

Q: 3. Let G = Z4xZ7. a. Determine all the generators for G. b. Determine a subgroup for each order 14,…

A: Step 1:Step 2:Step 3:Step 4:

Q: 5. List the left and right cosets of the subgroups in each of the following. Show Transcribed Text…

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