Talk:Partially ordered group
It seems easy to verify that if an ordered group is finite, the order has to be equality; i.e., apart from this trivial case an ordered group is infinite. If we have a source we should add this.--Patrick 07:52, 18 May 2007 (UTC)
Moreover, every element in the positive cone apart from the identity element has infinite order.--Patrick 08:04, 18 May 2007 (UTC)
[edit] + for multiplication?
Why is + being used for multiplication here? As far as I know, orderability has nothing to do with abelian groups, so this notation is just...wrong.
Unless someone can come up with a good reason I will change this notation to be multiplication, as is standard.
Farpov (talk) 12:57, 5 August 2010 (UTC)
I would like to point out that the if and only if statement in the introduction of the article assumes G to be commutative as well. The correct statement for non-commutative G is: for all a,b in G: a<=b iff (-a*b is in G or b*-a is in G). Not assuming this results in the statement being false for all groups with non trivial centralizor!
I thus completely agree with Farpov. — Preceding unsigned comment added by 82.170.166.152 (talk) 20:29, 23 February 2012 (UTC)
