Suppose thatf:G G such that f(x) and only if - axa. Then f is a group homomorphism if O a^2 = e a = e a^4 = e a^3 = e

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A: Here we check associativity property.

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A: The solution to the given question is explained below.

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Q: Suppose thatf: G → G such that f(x) = axa². Then f is a group homomorphism if and only if ) a^2 = e…

A: Option C.

Q: Let G = (-1,1) and (x,y) --> x ○ y = x + y/1 + xy is a binary operation on G. Let R+ = (0, ∞), with…

A: Given: G,O  with G=(-1, 1) ,  (x, y)→ x O y = x+y1+xy   and ℝ+, ·, ℝ+ = (0, ∞) with standard…

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Q: 3. Let f : (R\{0},-) (R\{0}, -) be group homomorphism defined by f(a) = |a|. Then ker(f) %3D =...

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Q: Suppose that f: G → G such that f(x) = axa. Then fis a group homomorphism if and only if a^2= e a =…

A: Since f is a group homomorphism , where f(x)=a∗x∗a−1,    x∈G. So a^-1=a implies self inverse implies…

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A: see my attachments

Q: evaluate using the Squeeze Theorem.

A: We know that cos is always between -1 and 1 Then we multiply all sides by (2t-1) and take limit

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A: Lets solve the question.

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Q: Suppose that f:G G such that f(x) = axa'. Then f is a group homomorphism if and only if O a^2 = e O…

A: We will use property of homomorphism to solve the following question

Q: let G={h: [0,1] approaches to R: h has an infinite number of derivatives). then G is a group under…

A: We need to find f inverse of (g) and show it is a coset of ker(f).

Q: Suppose that f: G → G such that f(x) = axa. Then fis a group homomorphism if and only if a = e O a^4…

A: Given that f:G→G be a function such that fx=axa

Q: Suppose that f: G → G such that f(x) and only if = axa. Then f is a group homomorphism if a = e a^4…

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Q: Suppose that f: G → G such that f(x) = axa. Then f is a group homomorphism if and only if a = e O…

A: From the condition of group homomorphism we can solve this.

Q: (G, .> be a group such that a.a = e for all a E G. Show that G is an abelian grou 2. Let

A: We have to solve given problem:

Q: Suppose that f: G → G such that f(x) = axa. Then f is a group homomorphism if and only if a = O a^4…

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Q: Suppose that f: G → G such that f(x) = axa. Then fis a group homomorphism if and only if a^4 = e a^3…

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

Q: Suppose that f: G G such that f(x) and only if = axa. Then f is a group homomorphism if -> a = e a^3…

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Q: Q3: Describe the quotient group of a- (²/z, ·+) b- (2/z,+)

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Q: Suppose that f:G-G such that f(x)- axa. Then fis a group homomorphism if and only if O a*2e O an4e O…

A: Here we will evaluate the required condition.

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Q: 5. Prove that the cyclic group Z/15Z is isomorphic to the product group Z/3Z × Z/5Z.

A: Definitions: Isomorphism: A mapping between two sets is called an isomorphism if it is one-to-one,…

Q: Suppose that f:G - G such that f(x) = axa". Then fis a group homomorphism if and only if O a^3 = e a…

A: f:G→G such that  fx=axa2 We know that f is a homomorphism if fxy=fxfy for all x, y∈G

Q: 3. Show that Q has no subgroup isomorphic to Z2 × Z2.

A: The objective is to show that ℚ has no subgroup isomorphic to ℤ2×ℤ2

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Q: Let GL(2,R) be the general linear group of 2 by 2 matrices. 1 x is a) Show that o: R GL (2,R) where…

A: We first prove this is a homomorphism.

Q: Let an for all n e N. Working directly from the Vn+1 definition show that limn- An = 1.

A: To evaluate limn→∞ nn+1: Here, an=nn+1 an can also be written as: an=1n+1n Simplifying this we get,…

Q: 22. Prove that the set = {(₁ ~ ) 1} x) | : x, y ≤ R, x² + y² = 1 = SO(2) = forms an abelian group…

A: Given: 22. SO(2)=x-yyx : x, y∈ℝ, x2+y2=1 To show: The given set is a group with respect to…

Q: Suppose that f:G G such that f(x) : and only if = axa. Then fis a group homomorphism if a^2 = e

A: A mapping f from a group (A,.)  to a group (B,*) is called a group homomorphism if f preserves the…

Q: Suppose that f:G →G such that f(x) = axa'. Then f is a group homomorphism if %3| and only if a = e…

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Q: Find the Galois group of the polynomial r-1.

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