Eine Bemerkung über die Gruppen PGL(2,F). (A remark on the groups PGL(2,F))
The author proves the following theorem: A KT-field \((F,+,\cdot,\sigma)\) is a commutative field iff the set \(R:=\{x\sigma (x^{-1})|\) \(x\in F^*\}\) is contained in the center of \((F^*,\cdot)\). Because of the unique connection between KT-fields and sharply 3-transitive groups one also gets an analogous characterisation of PGL(2,F).
scientific article; zbMATH DE number 4136199