H is a normal subgroup of the group G. Find the order of the quotient group G/H. Write out the distinct elements of G/H and construct a multiplication table for G/H. The alternating group G = A4; H = {(1), (1,2)(3, 4), (1, 3)(2, 4), (1, 4)(2, 3)}

Q: 2. Give a multiplication table for the group U(12).

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Q: Which of the following are subgroups of the group Z×11: {1,3,4,5,9}, {1,3,5,7,8}, {1,8},  {1,10},…

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Q: Which of the following groups are solvable groups: Z/nZ, D8, and S4.

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Q: 5. In each of parts (a) to (c) show that for the specified group G and subgroup A of CG (A) = A and…

A: (a) We are given that G=S3A=1,1 2 3,1 3 2 Now, we can see that 1 21 2 31 2-1=1 21 2 31 2=1 3 2 and 1…

Q: 4.1. Let a and b be elements of a group G. Assume that a has order 7 and that a³b = ba³. Prove that…

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Q: Qs: A. Define the symmetric group S3. Then find 1. Cent(S3) 2. All normal subgroups of S3 3. A3 4.…

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Q: Consider the group G=A4. List the elements of A4 in cycle notation, and determin the order of A4.

A: Consider the group G=A4.  We have to list the elements of A4 in cycle notation, and we have to…

Q: Determine whether or not the group (S3, ∘) is isomorphic to the group (T, ∘)

A: Two groups are given to us as ⇒S3,∘T,⊙ Therefore, both the sets S3, T are forming groups with…

Q: Let G be a group and let a e G. In the special case when A = {a}, we write Cg(a) instead of Cg({a})…

A: The given problem is related with group theory. G is a group and a ∈ G. Here, we write Cga instead…

Q: D5. (2) Determine the class equation for the group A4.

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Q: ic group, order of a group/element 1. Write a definition of a cyclic group. Provide two examples of…

A: We have to write the definition of cyclic group.

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: Let G be a group of order 3 and identity e. If the other elements are a and b, use the Latin square…

A: G be a group of order 3 Consider G=e,a,bwhere e is the identity then the Cayley table is…

Q: Q 5 The order of the element (123) of the group (S3,0) is (a) 1 (b) 2 (c) 3 (d) 00 Q 6 The order of…

A: Q.5. order of (123) in (S3,∘) is 3 (option (c) is true). since (123)∘(123)∘(123) = (123)∘(132) =…

Q: find the order of the cyclic group of the given group generated by the indicated element. The…

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