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

Part of: Projective and enumerative geometry Structure and classification of infinite or finite groups Permutation groups

Published online by Cambridge University Press:  22 February 2019

YATIR HALEVI  and
ITAY KAPLAN
YATIR HALEVI*
Affiliation:
Einstein Institute of Mathematics, Edmond J. Safra Campus, The Hebrew University of Jerusalem, Givat Ram 91904, Jerusalem, Israel
ITAY KAPLAN
Affiliation:
Einstein Institute of Mathematics, Edmond J. Safra Campus, The Hebrew University of Jerusalem, Givat Ram 91904, Jerusalem, Israel
*
e-mails: yatir.halevi@mail.huji.ac.il, kaplan@math.huji.ac.il
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Abstract

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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.

MSC classification

Primary: 14N99: None of the above, but in this section
Secondary: 20B27: Infinite automorphism groups 20E28: Maximal subgroups

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 168 , Issue 3 , May 2020 , pp. 601 - 612
Copyright
Copyright © Cambridge Philosophical Society 2019

Footnotes

†

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.

References

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