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Suppose that are cyclic groups of orders 6, 8, and 20,

Chapter 4, Problem 2E

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QUESTION:

Problem 2E

Suppose that are cyclic groups of orders 6, 8, and 20, respectively. Find all generators of .

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QUESTION:

Problem 2E

Suppose that are cyclic groups of orders 6, 8, and 20, respectively. Find all generators of .

ANSWER:

Step 1 of 3

It is known that for , then  only if  and vice versa.

Now, elements of  will be of the form .

So, we can say only if . Thus, . So the generators of  will come out to be .

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