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 December 21st, 2014, 08:29 AM #1 Newbie   Joined: Dec 2014 From: wales Posts: 2 Thanks: 0 abelian/cyclic groups What would be an example of a finite abelian group that is not cyclic?
December 21st, 2014, 11:20 AM   #2
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Quote:
 Originally Posted by jmorganj 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.

 January 4th, 2015, 12:37 AM #3 Newbie   Joined: Jul 2012 From: Houston, Texas Posts: 18 Thanks: 2 Math Focus: Geometry , Modern Algebra "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.
 January 7th, 2015, 07:26 AM #4 Newbie   Joined: Jan 2015 From: New York Posts: 5 Thanks: 0 One example is Z2*Z2 the direct sum of two Z2.

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