In geometry, a Moufang plane, named for Ruth Moufang, is a type of projective plane, more specifically a special type of translation plane. A translation plane is a projective plane that has a translation line, that is, a line with the property that the group of automorphisms that fixes every point of the line acts transitively on the points of the plane not on the line.[1] A translation plane is Moufang if every line of the plane is a translation line.[2]
^That is, the group acts transitively on the affine plane formed by removing this line and all its points from the projective plane.
a Moufangplane, named for Ruth Moufang, is a type of projective plane, more specifically a special type of translation plane. A translation plane is...
several concepts in mathematics are named: Moufang–Lie algebra Moufang loop Moufang polygon Moufangplane David Moufang (born 1966), German ambient techno musician...
Ruth Moufang (10 January 1905 – 26 November 1977) was a German mathematician. She was born to German chemist Eduard Moufang and Else Fecht Moufang. Eduard...
In mathematics, Moufang polygons are a generalization by Jacques Tits of the Moufangplanes studied by Ruth Moufang, and are irreducible buildings of...
mathematics, a Moufang loop is a special kind of algebraic structure. It is similar to a group in many ways but need not be associative. Moufang loops were...
necessarily associative, division algebras like the octonions correspond to Moufangplanes. There is no known purely geometric proof of the purely geometric statement...
translation planes that have at least two translation lines. Every finite Moufangplane is Desarguesian and every Desarguesian plane is a Moufangplane, but...
Slin'ko, Shestakov, and Shirshov. The projective plane over any alternative division ring is a Moufangplane. Every composition algebra is an alternative...
Non-Desarguesian Planes", Notices of the AMS, 54 (10): 1294–1303 Near-field Semifield Alternative division ring Hall systems (Hall planes) Moufangplane Quasifields...
Cayley plane (or octonionic projective plane) P2(O) is a projective plane over the octonions. The Cayley plane was discovered in 1933 by Ruth Moufang, and...
p. 306-318. R. Artzy: The Conic y = x 2 {\displaystyle y=x^{2}} in MoufangPlanes, Aequat.Mathem. 6 (1971), p. 31-35 E. Berz: Kegelschnitte in Desarguesschen...
definitions of conics can produce non-isomorphic objects in (infinite) Moufangplanes. Coxeter 1964, p. 60 Garner 1979, p. 132 Coxeter and several other authors...
not known what the optimal values of C and K are. Projective geometries Moufang polygon Schläfli double six Reye configuration Cremona–Richmond configuration...
symmetric spaces. Following Ruth Moufang's discovery in 1933 of the Cayley projective plane or "octonionic projective plane" P2(O), whose symmetry group is...
way. Generalized polygons satisfying a technical condition known as the Moufang property have been completely classified by Tits and Weiss. Every generalized...
Desargues configuration played a special role. Further work was done by Ruth Moufang and her students. The concepts have been one of the motivators of incidence...
23 problems. Dehn's doctoral students include Ott-Heinrich Keller, Ruth Moufang, and Wilhelm Magnus; he also mentored mathematician Peter Nemenyi and the...
multiplication operation making them not into a group but rather a loop, in fact a Moufang loop. For visualization this 8-dimensional polytope is often displayed...
the original on 2016-03-05. Retrieved 2015-09-01. See Magnus, Wilhelm; Moufang, Ruth (1954). "Max Dehn zum Gedächtnis". Mathematische Annalen. 127 (1):...
of O do not form a group. They do, however, form a loop, specifically a Moufang loop. The commutator of two octonions x and y is given by [ x , y ] = x...
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