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

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

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...

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Veröffentlicht in:Mathematical proceedings of the Cambridge Philosophical Society 2020-05, Vol.168 (3), p.601-612
Hauptverfasser: HALEVI, YATIR, KAPLAN, ITAY
Format: Artikel
Sprache:eng
Schlagworte:
Permutations
Theorems
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Zusammenfassung: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.
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004119000021