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Hall plane

In mathematics, a Hall plane is a non-Desarguesian projective plane constructed by Marshall Hall Jr. (1943). There are examples of order p2n for every prime p and every positive integer n provided p2n > 4.

Hall plane of order 9, Derivation & Properties

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Hall plane of order 9

4 related topics

Derivation

3 related topics

Properties

3 related topics

Algebraic construction via Hall systems

2 related topics

Key facts & relationships

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Automorphisms
28 × 35 × 5
Lenz–Barlotti class
IVa.3
Line orbit lengths
1, 90
Order
9
Point orbit lengths
10, 81
Properties
Translation plane

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Overview

Algebraic construction via Hall systems

Derivation

Properties

Hall plane of order 9

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Map overview Semantic statistics

Hall plane

Nodes26
Edges25
Triples41
Avg. degree1.92
Density0.076923
Components1

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Hall plane

Top relations

related to Construction · 10
Hall plane → Hall, Joseph Wedderburn, Oswald Veblen, The, There, This, Three, Veblen, Wedderburn, While
related to Derivation · 10
Hall plane → Another, Baer, Define, Desarguesian, Hall, Let, Ostrom, Start, The, We
related to Algebraic construction via Hall systems · 6
Hall plane → Extend, Galois, GF, Hall, The, To
related to Hall plane of order 9 · 4
Hall plane → Desarguesian, Hall, Hughes, The Hall
related to Properties · 4
Hall plane → All, André, Fano, Hall
Automorphisms · 1
Hall plane → 28 × 35 × 5
Lenz–Barlotti class · 1
Hall plane → IVa.3
Line orbit lengths · 1
Hall plane → 1, 90
Order · 1
Hall plane → 9
Point orbit lengths · 1
Hall plane → 10, 81

Important terminology Word statistics

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Important terminology

hall plane order planes quasifield projective unitals construction line finite derivation point translation properties called subplanes every prime automorphism group

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Hall planeAutomorphisms28 × 35 × 51.00infobox
Hall planeLenz–Barlotti classIVa.31.00infobox
Hall planeLine orbit lengths1, 901.00infobox
Hall planeOrder91.00infobox
Hall planePoint orbit lengths10, 811.00infobox
Hall planePropertiesTranslation plane1.00infobox
Hall planeis anon-Desarguesian projective plane constructed by Marshall Hall Jr0.90text
Hall planerelated to Algebraic construction via Hall systemsThe0.60section
Hall planerelated to Algebraic construction via Hall systemsHall0.60section
Hall planerelated to Algebraic construction via Hall systemsTo0.60section
Hall planerelated to Algebraic construction via Hall systemsGalois0.60section
Hall planerelated to Algebraic construction via Hall systemsGF0.60section

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    Min side: 3
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