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A generalisation of von Staudt’s theorem on cross-ratios

  • YATIR HALEVI (a1) and ITAY KAPLAN (a1)
Abstract

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.

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Footnotes
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Supported by the European Research Council grant 338821, by ISF grant No. 181/16 and ISF grant No. 1382/15.

Supported by the Israel Science Foundation grants no. 1533/14 and 1254/18.

Footnotes
References
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[vS47] von Staudt, K. G. C.. Geometrie der Lage (Verlag von Bauer und Raspe (Julius Merz), Nürnberg, 1847).
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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