All Questions
Tagged with gr.group-theory incidence-geometry
9 questions
10
votes
1
answer
356
views
Is the group of translations of an affine plane always commutative?
$\DeclareMathOperator\Dil{Dil}\DeclareMathOperator\Trans{Trans}\DeclareMathOperator\Col{Col}$An affine plane is a set of points $X$ endowed with a family $\mathcal L$ of subsets of $X$, called lines, ...
- 42k
2
votes
1
answer
120
views
Ree groups and Moufang octagons
Consider a Ree group of type $^2\mathrm{F}_4$, defined over the field $k$. Tits showed that every Moufang generalized octagon arises as a natural geometric module on which a Ree group of this type ...
- 4,605
16
votes
1
answer
395
views
Geometric interpretation of the exceptional isomorphism $PSp(4,3)=PSU(4,2^2)$
It is well-known that there is an isomorphism between $PSp(4,3)$ (the symplectic group of dimension $4$ over $\mathbb F_3$) and $PSU(4,2^2)$ (the unitary group defined by $4\times4$ unitary matrices ...
- 9,501
10
votes
1
answer
381
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About the paper by Buekenhout, Delandtsheer, Doyen, Kleidman, Liebeck and Saxl
The paper by Buekenhout, Delandtsheer, Doyen, Kleidman, Liebeck and Saxl called Linear spaces with flag transitive automorphism groups (Geom. Dedicata) from 1990 annonces a very powerful ...
- 2,287
14
votes
0
answers
552
views
Who conjectured that a transitive projective plane is Desarguesian?
The only known finite projective plane with a transitive automorphism group is the Desarguesian plane $PG(2,q)$ and it seems likely that there are no others, although this is not (quite) proved.
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- 12.7k
4
votes
1
answer
802
views
What is the automorphism group of this geometry?
Define the following incidence structure of rank three. The points are the elements of $\mathbb{Z}_7=$ {$0,\ldots,6$}. The lines of type 1 are the triples $(x,x+1,x+3)$ modulo $7$. The lines of type 2 ...
- 499
7
votes
1
answer
416
views
A rank 3 geometry for the sporadic simple group of Suzuki
I am actually studying coset geometries (in the sense of Tits and Buekenhout) for the sporadic simple group of Suzuki. I came aware that Buekenhout found in 1979 a geometry over the following diagram
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- 499
5
votes
2
answers
1k
views
Geometric interpretation of $BN$-pairs
My question is relative to a geometric interpretation of the $BN$-pairs that arise in Tits' theory of buildings. Here is a definition that comes from an article by G. Stroth (Nonspherical spheres).
$[...
- 499
9
votes
2
answers
471
views
Can any properties of a ring other than being a field be captured by the geometry of its 2-dimensional free module?
Can any properties of a ring other than being a field be captured by the geometry of its 2-dimensional free module?
Background:
In his wonderful, wonderful book Geometric Algebra, Emil Artin describes ...
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