Purchase Solution

Order of Elements, Factor Groups and Homomorphisms

Not what you're looking for?

Ask Custom Question

Help with this linear transformation problem. Please help with the following problem. Provide step by step calculations.

A. What is the order of the element 14 + <8> in the factor group Z24 / <8>?

I know that if I let G = Z24 and H = <8> , then H = <8> = {0,8,16}.
So Z24/<8> = {0+H,1+H,2+H,3+H,4+H,5+H,6+H,7+H}.

b. Prove or disprove: The map x --> 3x is a homomorphism from Z4 to Z6 .

Please see the attached file for the fully formatted problems.

Purchase this Solution
Solution Summary

Order of Elements, Factor Groups and Homomorphisms are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question. Step by step calculations are given.

Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

a. What is the order of the element 14 + in the factor group ?

I know that if I let G = and H = , then H = = . So = . However I'm not sure
what the order of 14 + is. I can't figure out what its ...

Purchase this Solution
Free BrainMass Quizzes
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.

Probability Quiz

Some questions on probability

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Multiplying Complex Numbers

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

View More Free Quizzes
Related BrainMass Solutions

  • Homomorphisms and Mapping Prime Elements

    97136 Homomorphisms and Mapping Prime Elements Let G and H be two finite cyclic groups of relatively prime orders. Determine the number of homomorphisms from G to H. The number of such homomorphisms is zero (0). ---------- Why?

  • Some Problems Involving Homomorphisms of Abelian Groups

    By the fundamental theorem of finite abelian groups [1], we know that G is the direct product of a finite number of cyclic groups, each of prime power order. Now G(p) is the set of all elements of each cyclic group whose order is a power of p.

  • Direct Products, Mappings and Homomorphisms

    a) Assume all phi_ji are group homomorphisms. Show that P is a subgroup of the direct product of the groups A_i. b) Assume I=Z+ and phi_ji are group homomorphisms.

  • Homomorphisms

    96941 Find the number of homomorphisms from 2 finite cyclic groups. The question is: Let G and H be two finite cyclic groups of relatively prime orders. Determine the number of homomorphisms from G to H.

  • Group Theory : Homomorphisms, Kernels, Isomorphisms and Fields

    39076 Group Theory : Homomorphisms, Kernels, Isomorphisms and Fields (a) If G1 and G2 are groups, define what it means to describe a function h:G1 -> G2 as a homomorphism. (b) If h: G1 ?

  • Direct Products of Groups, Conjugate Subgroups, Homomorphisms and Isomorphisms

    100792 Direct Products of Groups, Conjugate Subgroups, Homomorphisms and Isomorphisms Assume that K is a cyclic group, H is an arbitrary group and f1 and f2 are homomorphisms from K into Aut(H) such that f1(K) and f2(K) are conjugate subgroups of Aut

  • Homomorphisms

    29366 Homomorphisms ? Let G be a group and let a,b be two elements of G. The conjugate of b by a is, by definition, the element . The centralizer of a, denoted by s the set of all elements g in G such that ga=ag.

  • Group homomorphisms

    (b) Choose one of the nonzero formulas in part (a), and for this formula find the kernel and image, and show how elements of the image correspond to costs of the kernel. Please see attached file.

  • R-modules

    This solution demonstrates how to prove that a set of R-module homomorphisms are abelian groups.

View More Related Solutions