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Verify that Z4 (operation Ell) is isomorphic to Z; (operation 0). (See Example 11.4.)

Chapter 18, Problem 18.12

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QUESTION:

Verify that Z4 (operation Ell) is isomorphic to Z; (operation 0). (See Example 11.4.)

Questions & Answers

QUESTION:

Verify that Z4 (operation Ell) is isomorphic to Z; (operation 0). (See Example 11.4.)

ANSWER:

Step 1 of 3

It is need to prove that there is an isomorphism from the group  to the group  

Now,

 

And,

 

In the group, we observe the following things.

         

From the above equations, we observe that

         

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