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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

A characterization of the projective line

Author(s): B. Requejo; Juan B. Sancho
Journal: Proc. Amer. Math. Soc. 133 (2005), 3097-3101.
MSC (2000): Primary 51A05
Posted: March 24, 2005
MathSciNet review: 2159790
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Abstract | References | Similar articles | Additional information

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:

1.
E. Artin, ``Geometric Algebra'', Interscience, New York, 1957. MR 0082463 (18:553e)

2.
A.D. Gottlier and J. Lipman, Group-theoretic axioms for projective geometry, Canad. J. Math. 43(1) (1991), 89-107. MR 1108915 (92g:51002)

3.
J. Lipman, Definition of affine geometry by a group of transformations, Canad. Math. Bull. 4 (1961), 265-278. MR 0131194 (24:A1047)

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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: 10.1090/S0002-9939-05-07878-0
PII: S 0002-9939(05)07878-0
Received by editor(s): December 1, 2003
Received by editor(s) in revised form: May 20, 2004
Posted: March 24, 2005
Communicated by: Michael Stillman
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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