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Math / Contemporary Abstract Algebra 8 / Chapter 9 / Problem 12E

Contemporary Abstract Algebra | 8th Edition | ISBN: 9781133599708 | Authors: Joseph Gallian

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Prove that a factor group of a cyclic group is cyclic.

Chapter 9, Problem 12E

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QUESTION:

Prove that a factor group of a cyclic group is cyclic.

Questions & Answers

QUESTION:

Prove that a factor group of a cyclic group is cyclic.

ANSWER:

Step 1 of 3

As given by the question

It is given that the statement from the question, a factor group of a cyclic group is cyclic.

Now,

The objective is to prove a factor group of a cyclic group in cyclic.

Then,

A subgroup H of a group G is normal if and only if

For all

Another equivalent condition for H to be normal is that

That is,

For every

And

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