Question

a) Define a map  from a binary structure to the binary structure , where  is the usual multiplication,...

a) Define a map  from a binary structure to the binary structure , where  is the usual multiplication, by .

(i) Show that  is one-to-one and onto.

(ii) Give a precise formulation of  such that  is an isomophism.

b) Let be a group isomorphism. Prove that  is also a group isomorphism.

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 S={(0,1),(1,1),(3,-2)} ⊂ R², where R² is a real vector space with the usual vector addition...
Let S={(0,1),(1,1),(3,-2)} ⊂ R², where R² is a real vector space with the usual vector addition and scalar multiplication. (i) Show that S is a spanning set for R²​​​​​​​ (ii)Determine whether or not S is a linearly independent set
Let f be a function which maps from the quaternion group, Q, to itself by f...
Let f be a function which maps from the quaternion group, Q, to itself by f (x) = i ∙x, for i∈ Q and each element x in Q. Show all work and explain! (i) Is ? a homomorphism? (ii) Is ? a 1-1 function? (iii) Does ? map onto Q?
Fix a positive real number c, and let S = (−c, c) ⊆ R. Consider the...
Fix a positive real number c, and let S = (−c, c) ⊆ R. Consider the formula x ∗ y :=(x + y)/(1 + xy/c^2). (a)Show that this formula gives a well-defined binary operation on S (I think it is equivalent to say that show the domain of x*y is in (-c,c), but i dont know how to prove that) (b)this operation makes (S, ∗) into an abelian group. (I have already solved this, you can just ignore) (c)Explain why...
(a) This exercise will give an example of a connected space which is not locally connected....
(a) This exercise will give an example of a connected space which is not locally connected. In the plane R2 , let X0 = [0, 1] × {0}, Y0 = {0} × [0, 1], and for each n ∈ N, let Yn = {1/n} × [0,1]. Let Y = X0 ∪ (S∞ n=0 Yn). as a subspace of R 2 with its usual topology. Prove that Y is connected but not locally connected. (Note that this example also shows that...
This laboratory assignment involves implementing a data structure called a map. A map associates objects called...
This laboratory assignment involves implementing a data structure called a map. A map associates objects called keys with other objects called values. It is implemented as a Java class that uses arrays internally. 1. Theory. A map is a set of key-value pairs. Each key is said to be associated with its corresponding value, so there is at most one pair in the set with a given key. You can perform the following operations on maps. You can test if...
let g be a group. Call an isomorphism from G to itself a self similarity of...
let g be a group. Call an isomorphism from G to itself a self similarity of G. a) show that for any g ∈ G, the map cg : G-> G defined by cg(x)=g^(-1)xg is a self similarity group b) If G is cyclic with generator a, and sigma is a self similarity of G, prove that sigma(a) is a generator of G c) How many self-similarities does Z have? How many self similarities does Zn have? How many self-similarities...
n x n matrix A, where n >= 3. Select 3 statements from the invertible matrix...
n x n matrix A, where n >= 3. Select 3 statements from the invertible matrix theorem below and show that all 3 statements are true or false. Make sure to clearly explain and justify your work. A= -1 , 7, 9 7 , 7, 10 -3, -6, -4 The equation A has only the trivial solution. 5. The columns of A form a linearly independent set. 6. The linear transformation x → Ax is one-to-one. 7. The equation Ax...
1. Suppose we have the following relation defined on Z. We say that a ∼ b...
1. Suppose we have the following relation defined on Z. We say that a ∼ b iff 2 divides a + b. (a) Prove that the relation ∼ defines an equivalence relation on Z. (b) Describe the equivalence classes under ∼ . 2. Suppose we have the following relation defined on Z. We say that a ' b iff 3 divides a + b. It is simple to show that that the relation ' is symmetric, so we will leave...
5. Suppose that the incenter I of ABC is on the triangle’s Euler line. Show that...
5. Suppose that the incenter I of ABC is on the triangle’s Euler line. Show that the triangle is isosceles. 6. Suppose that three circles of equal radius pass through a common point P, and denote by A, B, and C the three other points where some two of these circles cross. Show that the unique circle passing through A, B, and C has the same radius as the original three circles. 7. Suppose A, B, and C are distinct...
Solutions for this exercise will not be posted. However, it is possible that questions from this...
Solutions for this exercise will not be posted. However, it is possible that questions from this exercise could appear on Midterm II. DEFINE ALL NOTATION!!!!! 1. Here is a pdf: . a) How do you know it is a continuous distribution? b) The constant a is positive. What is a? c) What is probability that the random variable X is equal to 1? d) What is F(-0.5)? e) What is the cdf of the random variable X? f) What is...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT