If G and H are groups with identities 16 and ¹H, respectively, and f:G ---> H is a homomorphism, then the kernel öf f is a. f(¹G) b. f(G) c. f-¹ (H) d. f-¹(1g) e. ¹H

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Q: 5. Let G be the multiplicative group {[2], [4], [6], [8]} = Z10-

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A: According to the given information, For part (a) it is required to show that:

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A: We will solve this by the help of isomorphism

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Q: 2. If a is an involution, then Baß is an involution for any transformation B.

A: It is given that α is an involution. So, we can say that α2=I.

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

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A: a) Given that the groups are 2ℤ,+ and 3ℤ,+.The function is given by φ:2ℤ→3ℤ and can be defined as…

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A: This is related to isomorphism

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A: To prove the required properties of a group homomorphism

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A: We have to solve given problem:

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Q: Help: Let G and G' be groups with identity elements e and e' respectively and let f:G goes to G' be…

A: Let G and G' be groups with identity elements e and e' respectively and let f:G goes to G' be a…

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A: We will use the definition of isomorphism to prove that the composition of two isomorphisms is again…

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A: Consider the given information: Let f:ℝ,+→(ℝ,+) be defined by, f(x) =3x-3 To find that f is an…

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Q: Let Ø: Z50 → Z15 be a group homomorphism with Ø(x) = 4x. Ø-1(4) None of the choices O {1, 16, 31,…

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Q: 6. Let G be GL(2, R), the general linear group of order 2 over R under multiplication. List the…

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Q: 5. Let G be a group and define z" z * *** *z for n factors c, where z E G and n E Z+. (a) Suppose…

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A: First we have to show that f:G→G' is homomorphism or not. To show homomorphism, we have to show…

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Q: 1. (10 points) Show that if ƒ : G → H is an isomorphism of groups G and H then ƒ-l (the inverse…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…