A generalisation of von Staudt's theorem that every permutation of the projective line that preserves harmonic quadruples is a projective semilinear map is given. It is then concluded that any proper supergroup of permutations of the projective semilinear group over an algebraically closed field of transcendence degree at least 1 is 4-transitive.
|Number of pages
|Mathematical Proceedings of the Cambridge Philosophical Society
|Published - 2020
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Copyright © Cambridge Philosophical Society 2019.
- 2010 Mathematics Subject Classification: 14N99 20B27 20E28