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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A characterization of the projective line


Authors: B. Requejo and Juan B. Sancho
Journal: Proc. Amer. Math. Soc. 133 (2005), 3097-3101
MSC (2000): Primary 51A05
DOI: https://doi.org/10.1090/S0002-9939-05-07878-0
Published electronically: March 24, 2005
MathSciNet review: 2159790
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Abstract: Let $X$ be a set (with at least three different points) and let $G$ be a group of bijections of $X$. If the action of $G$ on $X$ satisfies three natural conditions, then $X$ admits a canonical structure of a projective line over a commutative field, such that $G$ is the group of all projective transformations of $X$.


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Additional Information

B. Requejo
Affiliation: Departamento de Matemáticas, Universidad de Extremadura, 06071 Badajoz, Spain
Email: brequejo@unex.es

Juan B. Sancho
Affiliation: Departamento de Matemáticas, Universidad de Extremadura, 06071 Badajoz, Spain
Email: jsancho@unex.es

DOI: https://doi.org/10.1090/S0002-9939-05-07878-0
Received by editor(s): December 1, 2003
Received by editor(s) in revised form: May 20, 2004
Published electronically: March 24, 2005
Communicated by: Michael Stillman
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.