Prove that there is no homomorphism from Z1, O Z, onto Z, O Z,.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
Prove that there is no homomorphism from Z1, O Z, onto Z, O Z,.
Transcribed Image Text:Prove that there is no homomorphism from Z1, O Z, onto Z, O Z,.
Expert Solution
Step 1: To prove:

There is no homomorphism from Z subscript 16 circled plus Z subscript 2 onto Z subscript 4 circled plus Z subscript 4.

Step 2: Concept used:

According to the First isomorphism theorem, if phi colon space G space rightwards arrow G with bar on top is a homomorphism, then fraction numerator G over denominator k e r ϕ end fraction almost equal to ϕ left parenthesis G right parenthesis be the isomorphism given by g text ker end text ϕ rightwards arrow ϕ left parenthesis g right parenthesis



steps

Step by step

Solved in 4 steps with 24 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,