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Solved: What is the smallest positive integer n such that
Chapter 11, Problem 2E(choose chapter or problem)
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.