A characterization of the projective line
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- by B. Requejo and Juan B. Sancho PDF
- Proc. Amer. Math. Soc. 133 (2005), 3097-3101 Request permission
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 $X$.References
- E. Artin, Geometric algebra, Interscience Publishers, Inc., New York-London, 1957. MR 0082463
- Alex D. Gottlieb and Joseph Lipman, Group-theoretic axioms for projective geometry, Canad. J. Math. 43 (1991), no. 1, 89–107. MR 1108915, DOI 10.4153/CJM-1991-006-2
- Joe Lipman, Definition of affine geometry by a group of transformations, Canad. Math. Bull. 4 (1961), 265–278. MR 131194, DOI 10.4153/CMB-1961-030-1
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
- 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
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 3097-3101
- MSC (2000): Primary 51A05
- DOI: https://doi.org/10.1090/S0002-9939-05-07878-0
- MathSciNet review: 2159790