This problem is still bugging me... does anybody have any ideas?
Let be additive subgroups of both containing 1. Let be an order preserving group homomorphism such that . Show that for all .
The idea that I am working with is to let such that
then there exists an integer such that
.
now apply and get the following
and
and suppose that for all . In this way I hope to get some contradiction
Or is there another way?