Cyclic Abelian Groups: True for All Cases?

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is this true for all cases? i know something can be abelian and not cyclic. thanks
 
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It's not true, as you say: some can be abelian but not cyclic. So cyclic implies abelian but not necessarily the other way arround.
 
johnnyboy2005 said:
is this true for all cases? i know something can be abelian and not cyclic. thanks

do you perhaps mean implies instead of =?
 
yes. other wise my question answers itself. so cyclic implies abelian. thanks for the help.
 
you have proved this (elementary in the sense of asked on the first examples sheet of any course in group theory if at all) result...
 
I love this property.

You work with cyclic groups so often that it's so nice to have them all abelian. I love it. :)
 

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