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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 
Senior Member Joined: Aug 2012 Posts: 2,306 Thanks: 706  
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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