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There is a unique homomorphism e : Z6 -+ S3 such that e([I]) = (1 2 3). Determine

Chapter 21, Problem 21.18

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QUESTION:

There is a unique homomorphism e : Z6 -+ S3 such that e([I]) = (1 2 3). Determine e([k])for each [k] E Z6. Which elements are in Ker e?

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QUESTION:

There is a unique homomorphism e : Z6 -+ S3 such that e([I]) = (1 2 3). Determine e([k])for each [k] E Z6. Which elements are in Ker e?

ANSWER:

Step 1 of 3

The given that unique homomorphism  such that .

The group  is cyclic group generated by element . Then, the Homomorphic map of cyclic group is cyclic.

 

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