Purchase Solution

Group homomorphism

Not what you're looking for?

Ask Custom Question

Homomorphism
Problem 3:
Define µ : Z4 × Z6 -> Z4 × Z3 by
µ ([x]4,[y]6) = ([x+2y]4,[y]3).
(a) Show that µ is a well-defined group homomorphism.
(b) Find the kernel and image of µ, and apply the fundamental homomorphism theorem.

Attachments
Purchase this Solution
Solution Summary

This is a proof regarding a well-defined group homomorphism, and shows how to find kernel and image.

Solution Preview

Please see attached file.
Homomorphism
Problem 3:

Solution:

(a) If y1 y2 (mod 6), then 2y1 - 2y2 is divisible by 12, so

2y1 2y2 (mod 4), and then it ...

Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

View More Free Quizzes
Related BrainMass Solutions

  • Homomorphism of a Group and Kernel of the Homomorphism

    64420 Group Theory :Homomorphism of a Group: Verify if the mapping defined is a homomorphism and in that case in which it is homomorphism,determine the Kernel:G is the group of non-zero real numbers under multiplication, ¯G = G, phi(x) = x^2 all x belongs

  • Group and ring homomorphisms

    240814 Group and Ring Homomorphisms Please attached for the question to help me understand Group and Ring Homomorphisms. Is this function a Homomorphism?

  • Homomorphism of a Group and Kernel of the Homomorphism

    64572 Group Theory : Verify if the mapping defined is a homomorphism and in that case in which it is homomorphism,determine the Kernel : G is any abelian group and ¯G = G, phi(x) = x^5 all x belongs to G.

  • Identity Element Preserved in a Homomorphism

    38310 Identity Element Preserved in a Homomorphism Let ... be a homomorphism of a group ... into a group... . Show that if is the identity element of... , then is the identity element... in ... .

  • Group homomorphisms

    2417 Group homomorphisms Homomorphism Problem 1: Find all group homomorphisms from Z4 into Z10 Please see attached file.

  • Problems in Group Theory

    455433 Problems in Group Theory: Homomorphism Let G_1 and G_2 be groups and ?:G_1?G_2 a map. Which of the following is a group homomorphism? Explain your answers. If ? is a homomorphism, describe the kernel and the image of ?. a) G_1=C_4=?

  • Homomorphism and First Isomorphism Theorem

    Now I claim that is a group homomorphism. For any , we have Thus is a group homomorphism. Next we find . If , then , thus . Conversely, if , then we have by definition of . Thus .

  • Group homomorphisms

    2422 Group homomorphisms functions Homomorphism Problem 4: Let G, G1, and G2 be groups. Let µ1 : G -> G1 and µ2 : G -> G2 be group homomorphisms.

  • Groups : Isomorphism and Homomorphism

    A group homomorphism is investigated.

  • Homomorphism Subgroup Proofs

    Prove that the only homomorphism from G to H is the trivial homomorphism. (b) Give an example of a group G of size 77 and a group K of size 56 and a nontrivial homomorphism from G to IC.

View More Related Solutions