Question

True or False? If f : M → N is a homomorphism and a ∈ M,...

True or False? If f : M → N is a homomorphism and a ∈ M, then |a| = |f(a)|.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let N and H be groups, and here for a homomorphism f: H --> Aut(N) =...
Let N and H be groups, and here for a homomorphism f: H --> Aut(N) = group automorphism, let N x_f H be the corresponding semi-direct product. Let g be in Aut(N), and  k  be in Aut(H),  Let C_g: Aut(N) --> Aut(N) be given by conjugation by g.  Now let  z :=  C_g * f * k: H --> Aut(N), where * means composition. Show that there is an isomorphism from Nx_f H to Nx_z H, which takes the natural...
True or False...Provide your reasons If f(n) =o(g(n)), then f(n)=O(g(n)) If f(n) =O(g(n)), then f(n) ≤...
True or False...Provide your reasons If f(n) =o(g(n)), then f(n)=O(g(n)) If f(n) =O(g(n)), then f(n) ≤ g(n) 3.  If 1<a=O(na), then f(n)=O(nb) 4. A and B are two sorting algorithms. If A is O(n2) and B is O(n), then for an input of X integers, B can sort it faster than A.
State whether the statement is true or false. Also,please give a simple and clear explanation. A....
State whether the statement is true or false. Also,please give a simple and clear explanation. A. let a,b ∈Sn, then |ab| is the least common multiple of |a| and |b|. B.Let G and H be groups and suppose N is a normal subgroup of G. Then there exists a homomorphism from f: G → H,where N is the kernel of f.
True or False? No reasons needed. (e) Suppose β and γ are bases of F n...
True or False? No reasons needed. (e) Suppose β and γ are bases of F n and F m, respectively. Every m × n matrix A is equal to [T] γ β for some linear transformation T: F n → F m. (f) Recall that P(R) is the vector space of all polynomials with coefficients in R. If a linear transformation T: P(R) → P(R) is one-to-one, then T is also onto. (g) The vector spaces R 5 and P4(R)...
4. Let f : G→H be a group homomorphism. Suppose a∈G is an element of finite...
4. Let f : G→H be a group homomorphism. Suppose a∈G is an element of finite order n. (a) Prove that f(a) has finite order k, where k is a divisor of n. (b) If f is an isomorphism, prove that k=n.
Determine wether the statements are true or false 1. Suppose we have f(n) = nlgn ,...
Determine wether the statements are true or false 1. Suppose we have f(n) = nlgn , g(n) = 5n , then f(n) = O(g(n)). 2. Suppose we have f(n) = nn/4 , g(n) = n1/2lg4n , then f(n) = O(g(n)). 3. No comparison-based sorting algorithm can do better than Ω(n log n) in the worst-case 4. Quicksort running time does not depend on random shuffling.
Let M = { f: ℝ  → ℝ | f is continuous } be the ring of...
Let M = { f: ℝ  → ℝ | f is continuous } be the ring of all continuous functions from the real numbers to the real numbers. Let a be any real number and define the following function: Φa:M→R f(x)↦f(a) This is called the evaluation homomorphism. 1. Describe the kernel of the evaluation homomorphism. 2. Is the kernel of the evaluation homomorphism a prime ideal or a maximal ideal or both or neither?
Prove this statement: Let ϕ : A1 → A2 be a homomorphism and let N =...
Prove this statement: Let ϕ : A1 → A2 be a homomorphism and let N = ker ϕ. Then A1/N is isomorphic to ϕ(A1). Further ψ : A1/N → ϕ(A1) defined by ψ(aN) = ϕ(a) is an isomorphism. You must use the following elements to prove: - well-definedness - one-to-one - onto - homomorphism
Suppose G and H are groups and ϕ:G -> H is a homomorphism. Let N be...
Suppose G and H are groups and ϕ:G -> H is a homomorphism. Let N be a normal subgroup of G contained in ker(ϕ). Define a mapping ψ: G/N -> H by ψ (aN)= ϕ (a) for all a in G. Prove that ψ is a well-defined homomorphism from G/N to H. Is ψ always an isomorphism? Prove it or give a counterexample
Let φ : G → G′ be an onto homomorphism and let N be a normal...
Let φ : G → G′ be an onto homomorphism and let N be a normal subgroup of G. Prove that φ(N) is a normal subgroup of G′.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT