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Translation plane

In mathematics, a translation plane is a projective plane which admits a certain group of symmetries (described below). Along with the Hughes planes and the Figueroa planes, translation planes are among the most well-studied of the known non-Desarguesian planes, and the vast majority of known non-Desarguesian planes are either translation planes, or can…

Algebraic construction with coordinates, Algebraic construction with spreads (André) & Families of non-Desarguesian translation planes

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Algebraic construction with coordinates

Planar ternary ringQuasifieldNearfieldsSemifieldsMoufang planes
8 related topics

Algebraic construction with spreads (André)

Vector spaceFieldIncidence structureTranslationsProjective space
5 related topics

Families of non-Desarguesian translation planes

Subregular planesAndré planesNearfield planesSemifield planes
4 related topics

Geometric construction with spreads (Bruck/Bose)

SpreadHyperplaneDivision ring
3 related topics

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Overview

Algebraic construction with coordinates

Geometric construction with spreads (Bruck/Bose)

Algebraic construction with spreads (André)

Reguli and regular spreads

Families of non-Desarguesian translation planes

Finite translation planes of small order

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Map overview Semantic statistics

Translation plane

Nodes44
Edges43
Triples143
Avg. degree1.95
Density0.045455
Components1

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Translation plane

Top relations

related to References · 104
Translation plane → Algebra, Amer, American Mathematical Society, André, Arthur, Band, Berlin, BF00181513, BF01187370, BF01388504, BF01578865, Biliotti, Bose, Brendan, Canadian Journal, Catalonia, Chapman, CJM-1977-013-6, Class, CO
related to Algebraic construction with coordinates · 9
Translation plane → Cayley, Desarguesian, Every, For, However, Moufang, Nearfield, Semifield, Some
related to Geometric construction with spreads (Bruck/Bose) · 9
Translation plane → Bruck-Bose, Define, Embed PG, Given, In, PG, Sigma, Then, Translation
related to Algebraic construction with spreads (André) · 7
Translation plane → André, Bruck/Bose, Let, The, Then, Vi, Vj
related to Further reading · 7
Translation plane → Foundations, Johnson, Marcel Dekker ISBN, Mauro Biliotti, Norman, Translation Planes, Vikram Jha
related to Finite translation planes of small order · 6
Translation plane → Desarguesian, Finite, Hall, It, The, There
is a · 1
Translation plane → projective plane which admits a certain group of symmetries

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Important terminology

translation planes plane projective spread displaystyle order pg doi construction finite line 10 called 2n affine regular spreads bruck bose

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Translation planeis aprojective plane which admits a certain group of symmetries0.90text
Translation planerelated to Algebraic construction with coordinatesEvery0.60section
Translation planerelated to Algebraic construction with coordinatesFor0.60section
Translation planerelated to Algebraic construction with coordinatesHowever0.60section
Translation planerelated to Algebraic construction with coordinatesSome0.60section
Translation planerelated to Algebraic construction with coordinatesNearfield0.60section
Translation planerelated to Algebraic construction with coordinatesSemifield0.60section
Translation planerelated to Algebraic construction with coordinatesMoufang0.60section
Translation planerelated to Algebraic construction with coordinatesDesarguesian0.60section
Translation planerelated to Algebraic construction with coordinatesCayley0.60section
Translation planerelated to Algebraic construction with spreads (André)André0.60section
Translation planerelated to Algebraic construction with spreads (André)Bruck/Bose0.60section

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    Min side: 3
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