Cyclic Abelian Groups: True for All Cases?

johnnyboy2005 · Nov 28, 2005

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

TD · Nov 28, 2005

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 · Nov 28, 2005

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 =?

johnnyboy2005 · Nov 28, 2005

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

matt grime · Nov 28, 2005

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 · Dec 1, 2005

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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