On the simplicity of the multiplicative group of an existentially closed skew field (Q1290393)

Let \(Z\) be a commutative field and \(C\) the class of skew-fields with center \(Z\). It is shown that the group \(G=E^*/Z^*\) is simple. It is also proved, along with several other related results, that if \(Z\) is algebraically closed, then \(G\) is torsion-free and its elements other than the unit form a single conjugacy class. The proofs depend on a theorem due to P. M. Cohn, and the paper is written in honour of his 75-th Birthday. In the second equation of \((1,d)\), \(x\) should be replaced by \(t\).