On embedding left-ordered groups into division rings. (Q487143)

Left (or right) ordered groups have been studied first in the late fifties by Paul Conrad. The group ring \(F[G]\) of such a group \(G\) over a skew-field \(F\) has no zero divisors, but it is still open whether \(F[G]\) can always be embedded into a skew-field. Malčev and B. H. Neumann have proved this for fields \(F\) and (two-sided) totally ordered groups \(G\). Dubrovin obtained some extension to the one-sided case. In the paper under review, the authors simplify and extend previous results and provide interesting new examples. In particular, they deal with the problem of extending group automorphisms to automorphisms of the enveloping skew-field.