A Generalization of von Staudt's Theorem on Cross-Ratios

2018/03/22 by Yatir Halevi, Halevi, Yatir, Itay Kaplan +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO) #math.AG #math.GR #math.LO

paper · pdf · doi:10.48550/arxiv.1803.08520

arxiv created 2018/07/30 · arxiv updated 2018/07/31

Abstract

A generalization 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.

Related

• On distinct cross-ratios in positive characteristic
• Bochert's results on the minimal degree of multiply transitive permutation groups
• Cross-Ratios of Scheme-Valued Points
• The Projective Line as a Meridian
• Uniform (2,k)-generation of the 4-dimensional classical groups