7) Define a map ø1 from Z3 x Z → Z4 as follows: 01(m, n) = 4(m + n). Is ø1 a well-defined map? (If yes, prove it. If no, explain why it is not well defined) Is it a group homomorphism?(If yes, prove it. If no, explain why it is not a homomor- phism). If it is a homomorphism, what is ker(1).

7) Define a map ø1 from Z3 x Z → Z4 as follows: 01(m, n) = 4(m + n). Is ø1 a well-defined map? (If yes, prove it. If no, explain why it is not well defined) Is it a group homomorphism?(If yes, prove it. If no, explain why it is not a homomor- phism). If it is a homomorphism, what is ker(1).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

(7) Define a map ø1 from Z3 × Z → Z4 as follows: 01(m, n) = 4(m + n).
Is ø1 a well-defined map? (If yes, prove it. If no, explain why it is not well defined)
Is it a group homomorphism?(If yes, prove it. If no, explain why it is not a homomor-
phism).
If it is a homomorphism, what is ker(ø1).

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