Contemporary Abstract Algebra
9th Edition
ISBN: 9781305657960
Author: Joseph Gallian
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 10, Problem 16E
Prove that there is no homomorphism from
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionChapter 10 Solutions
Contemporary Abstract Algebra
Ch. 10 - Let R* be the group of nonzero real numbers under...Ch. 10 - Let G be the group of all polynomials with real...Ch. 10 - Prob. 7ECh. 10 - Explain why the correspondence x3x from Z12toZ10...Ch. 10 - Prob. 15ECh. 10 - Prove that there is no homomorphism from...Ch. 10 - Let be a homomorphism from a finite group G to G...Ch. 10 - Prob. 39ECh. 10 - Show that a homomorphism defined on a cyclic group...Ch. 10 - Suppose there is a homomorphism from G onto Z2Z2...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Similar questions
- Write 20 as the direct sum of two of its nontrivial subgroups.arrow_forwardLet G=1,i,1,i under multiplication, and let G=4=[ 0 ],[ 1 ],[ 2 ],[ 3 ] under addition. Find an isomorphism from G to G that is different from the one given in Example 5 of this section. Example 5 Consider G=1,i,1,i under multiplication and G=4=[ 0 ],[ 1 ],[ 2 ],[ 3 ] under addition. In order to define a mapping :G4 that is an isomorphism, one requirement is that must map the identity element 1 of G to the identity element [ 0 ] of 4 (part a of Theorem 3.30). Thus (1)=[ 0 ]. Another requirement is that inverses must map onto inverses (part b of Theorem 3.30). That is, if we take (i)=[ 1 ] then (i1)=((i))1=[ 1 ] Or (i)=[ 3 ] The remaining elements 1 in G and [ 2 ] in 4 are their own inverses, so we take (1)=[ 2 ]. Thus the mapping :G4 defined by (1)=[ 0 ], (i)=[ 1 ], (1)=[ 2 ], (i)=[ 3 ]arrow_forwardProve that if f is a permutation on A, then (f1)1=f.arrow_forward
- 6. Prove that if is a permutation on , then is a permutation on .arrow_forwardTrue or False Label each of the following statements as either true or false. The kernel of a homomorphism is never empty.arrow_forward22. Let be a ring with finite number of elements. Show that the characteristic of divides .arrow_forward
- 44. Consider the set of all matrices of the form, where and are real numbers, with the same rules for addition and multiplication as in. a. Show that is a ring that does not have a unity. b. Show that is not a commutative ring.arrow_forward31. Prove statement of Theorem : for all integers and .arrow_forwardProve statement d of Theorem 3.9: If G is abelian, (xy)n=xnyn for all integers n.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Elements Of Modern Algebra
Algebra
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Cengage Learning,
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Orthogonality in Inner Product Spaces; Author: Study Force;https://www.youtube.com/watch?v=RzIx_rRo9m0;License: Standard YouTube License, CC-BY
Abstract Algebra: The definition of a Group; Author: Socratica;https://www.youtube.com/watch?v=QudbrUcVPxk;License: Standard Youtube License