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December 21st, 2014, 08:29 AM   #1
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abelian/cyclic groups

What would be an example of a finite abelian group that is not cyclic?
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December 21st, 2014, 11:20 AM   #2
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Originally Posted by jmorganj View Post
What would be an example of a finite abelian group that is not cyclic?
There's one of order 4, can you think of it? Hint: It's a direct sum of two copies of the simplest nontrivial group you can think of.
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January 4th, 2015, 12:37 AM   #3
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"Every cyclic group G is Abelian" but every Abelian group G is not cyclic.

Example: U = {1,3,5,7} under multiplication modulo 8 is a noncyclic Abelian group
You can verify it by using the Cayley table.

Last edited by buiduchuy; January 4th, 2015 at 12:39 AM.
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January 7th, 2015, 07:26 AM   #4
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One example is Z2*Z2 the direct sum of two Z2.
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