Cyclic Abelian Groups: True for All Cases?

[johnnyboy2005]

is this true for all cases? i know something can be abelian and not cyclic. thanks

 

[TD]

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.

 

[matt grime]

is this true for all cases? i know something can be abelian and not cyclic. thanks

do you perhaps mean implies instead of =?

 

[johnnyboy2005]

yes. other wise my question answers itself. so cyclic implies abelian. thanks for the help.

 

[matt grime]

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...

 

[JasonRox]

I love this property.

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