Formally real fields with a simple description of the absolute Galois group (Q1089050)

Let R be a real closed field and k a subfield of R maximal with respect to the exclusion of some fixed element \(\alpha\in R\). The authors give a complete description of the absolute Galois group G(k) of such a field k. It turns out that there are essentially three types of profinite groups occurring, all of which are quite simple to describe. The authors also prove that, if such a group occurs as the absolute Galois group of a field k, then k admits a real closure R and is a maximal subfield of R excluding a fixed element \(\alpha\in R\).