Mehrfach transitive Operationen algebraischer Gruppen

All d-fold (d>1) transitive actions of algebraic groups defined over an algebraic closed field k are classified. The result: (G acts on X)

1. X is the n-dimensional projective space and G=PGL(n+1,k). This action is always doubly transitive and triply transitive for n=1.

2. X is the n-dimensional affine space and G=S L T, where S is a subgroup of the group of scalars, T is the group of translations, and L is either SL_n(k), Sp_n(k) (n even) or G_2 (n=6, char k=2) acting linearly. All these actions are doubly transitive.

This paper was my Diploma thesis in Erlangen.

Appeared in: Archiv der Mathematik 41 (1983) 438-446

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Last updated: August 19, 2006