Difference between revisions of "Fano postulate"
From Encyclopedia of Mathematics
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| − | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> H.S.M. Coxeter, "Introduction to geometry" , Wiley (1961)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> A.M. Gleason, "Finite Fano planes" ''Amer. J. Math.'' , '''78''' (1956) pp. 797–807</TD></TR></table> | + | <table> |
| + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> H.S.M. Coxeter, "Introduction to geometry" , Wiley (1961) {{ZBL|0095.34502}}</TD></TR> | ||
| + | <TR><TD valign="top">[a2]</TD> <TD valign="top"> A.M. Gleason, "Finite Fano planes" ''Amer. J. Math.'' , '''78''' (1956) pp. 797–807 {{ZBL|0072.38001}}</TD></TR> | ||
| + | </table> | ||
Latest revision as of 08:56, 13 April 2017
A proposition of projective geometry established by G. Fano (1892). It consists in the fact that the diagonal points of a quadrangle are not collinear. The Fano postulate is equivalent to the fact that the characteristic of the skew-field $K$ associated with the projective geometry in question is not equal to 2. The Fano postulate does not hold, for example, in the finite projective plane consisting of seven points and lines associated with the skew-field $K$ of the two elements 0 and 1.
Comments
On the other hand, it was shown by A.M. Gleason [a2] that a finite projective plane in which the diagonal points of any quadrangle are collinear, is a projective plane over a field (of characteristic 2).
References
| [a1] | H.S.M. Coxeter, "Introduction to geometry" , Wiley (1961) Zbl 0095.34502 |
| [a2] | A.M. Gleason, "Finite Fano planes" Amer. J. Math. , 78 (1956) pp. 797–807 Zbl 0072.38001 |
How to Cite This Entry:
Fano postulate. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Fano_postulate&oldid=40965
Fano postulate. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Fano_postulate&oldid=40965
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article