Die Gruppe der speziellen gebrochen-affinen Transformationen eines KT- Fastkörpers. (The group of special fractional affine transformations of a KT-nearfield)
The sharply 3-transitive groups with stabilizers containing a regular abelian normal subgroup can be described as the ``fractional linear'' groups T(N,\(\epsilon\)), where N is a nearfield with an inversion-like mapping \(\epsilon\), cf. \textit{H. Wähling} [Theorie der Fastkörper (Thales Verlag, Essen 1987; Zbl 0669.12014)] or \textit{W. Kerby} [On infinite sharply multiply transitive groups (Vandenhoeck \& Ruprecht, Göttingen 1974; Zbl 0291.20039)]. Let \(| N| >3\). The authors show that T(N,\(\epsilon\)) has a simple normal subgroup S(N,\(\epsilon\)), which is the smallest normal subgroup of T(N,\(\epsilon\)). Furthermore, if \(S(N_ 1,\epsilon_ 1)\) and \(S(N_ 2,\epsilon_ 2)\) are permutation- isomorphic, then \((N_ i,\epsilon_ i)\) are closely related (but not isomorphic in general). If char \(N\neq 2\) and if S(N,\(\epsilon\)) is permutation-isomorphic to PSL(2,F) for some field F, then N is a Dickson nearfield constructed from F, and \(\epsilon\) is the inversion of F.
scientific article; zbMATH DE number 4156740
scientific article