Purchase Solution

Kernel of Homomorphism

Not what you're looking for?

Ask Custom Question

Please see the attached file for the fully formatted problems.

Suppose  is an onto homomorphism from ℤ16 to a group G of order 4. Find ker(). Explain your answer.

Attachments
Purchase this Solution
Solution Summary

A kernel is found. The method is explained in detail.

Solution Preview

Please see the attachment.

: is a group homomorphism. is onto. Since is a cyclic ...

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

Understanding of how geometry applies to in real-world contexts

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Probability Quiz

Some questions on probability

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.

View More Free Quizzes
Related BrainMass Solutions

  • Prove that the Kernel of a homomorphism is a subspace.

    137567 Prove that the Kernel of a homomorphism is a subspace. Prove that the Kernel of a homomorphism is a subspace.

  • Homomorphism of a Group and Kernel of the Homomorphism

    Kernel of the Homomorphism 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

  • Group homomorphism

    (b) Find the kernel and image of µ, and apply the fundamental homomorphism theorem. 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=?

  • finite Abelian group

    Refer: http://en.wikipedia.org/wiki/Homomorphism 3. Kernel (of a homomorphism): The kernel of a homomorphism f : G -> H is the set of all elements of G which map to the identity element of H Let e' be the identity element of H.

  • Homomorphism and Kernel

    Prove that f is a homomorphism and find the kernel of f. Please see the attachment. This provides an example of proving f is a homomorphism and finding a kernel.

  • Homomorphism of a Group and Kernel of the Homomorphism

    Kernel of the Homomorphism 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

  • Group Theory : Homomorphisms, Kernels, Isomorphisms and Fields

    Prove that precisely two of the three functions below is a homomorphism. Identify the kernel and range of each of those that is a homomorphism.

  • Kernel and Homomorphism

    30955 Kernel and Homomorphism Here's my problem: If A and B are subsets of a group G, define AB = {ab | a 2 A, b 2 B}. Now suppose phi: G -> G0 is a homomorphism of groups and N = Ker(phi) is its kernel.

View More Related Solutions