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Solved: What is the smallest positive integer n such that

Chapter 11, Problem 2E

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QUESTION:

What is the smallest positive integer n such that there are three nonisomorphic Abelian groups of order n? Name the three groups.

Questions & Answers

QUESTION:

What is the smallest positive integer n such that there are three nonisomorphic Abelian groups of order n? Name the three groups.

ANSWER:

Step 1 of 2

Recall that the groups of prime order are cyclic only. So, for and , we have only cyclic groups.

Now, if , there is only one subgroup as  is the only factorization of 6.

This means there is only 1 external direct product of cyclic groups with order 6.

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