For the following problems, let G be a group with the following generators and relations: G = (a, b, cla² = b² = c² = abc) . Give the conjugacy classes of G. What does this tell you about the representation theory of G? (Hint: It helps to know the following facts can be derived about this group: The group has eight elements e, a, b, c, a², a³, 63, c³ with a4 = €, ab = c ba = c³, bc = a, cb=a3, cab and ac= := b³.)

Q: 4. Vnite the table for (Z₂ ©) and use it to show that (Z7, © ) is a group. 7 Find the inverse. of 2…

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Q: In the group S6, consider the elements 1 2 3 4 5 6 4 3 6 5 1 2 1 2 3 4 56 35 4 2 6 1 a = and B = (a)…

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Q: Consider the group (Zn,+). Find the center of Zn (ie. find Z (Zn)).

A: Center of the given group is Zn itself.Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Introduction of the problem: Let G = ℤ32 and H be the group of G generated by 4 Problem: Is G/H…

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Q: Updated the introduction of the problem. It was messed up. Introduction of the problem: Let G = D6…

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Q: The inverse of each element in the group ({1, 3, 5, 7}, ∙8)

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Q: How would you solve such a question: Suppose f : Z → Z5 is a group homomorphism, and suppose f (3) =…

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Q: Express the following as products of cyclic gr a) Z140 ») U (140) =) Z400 H) U (400).

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Q: Find the order of the given factor group (Z3 x Z6)/

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Q: For each of the following groups, find all the conjugacy classes and write out the conjugacy class…

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Q: (1).* 4 and |6| = 2, Let G be a group. Let a, b EG such that |a| and a b = ba. Then determine |ba|,…

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

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Q: Write down the six elements of S3 and give the multiplication table for the group. The six elements…

A: Given six elements of S3 are     1=123123, a=123231=123 , b=123312=132, c=123213=12, d=123321=13,…

Q: Hello, can you help me out with this problem? Please write a solution on a piece of paper and upload…

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Q: Determine the lim g x 4+ 3+ 2+

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Q: Express as a product. 1+ sin a

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Q: 3. consider the group D4 = {(1), (1234), (13), (24), (1432), (12), (34), (14), (23), (13), (24)} a.…

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