# Automorphism group of an ordered abelian group

Discussion in 'Math Research' started by Linus Kramer, Dec 3, 2003.

1. ### Linus KramerGuest

I have a question on automorphisms of ordered abelian
groups.

Suppose that M is a (divisible) ordered abelian group.
Then the automorphism group Aut(M) is in a natural way
partially ordered (put f \leq g if f(|x|)\leq g(|x|)
for all x in M).
Now my question is: is Aut(M) directed, i.e. given f,g in
Aut(M), is there an h in Aut(M) which is an upper bound for
f and g?

--Linus Kramer

Linus Kramer, Dec 3, 2003