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Results tagged with incidence-geometry
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user 12858
Abstract incidence geometries like projective spaces, polar spaces, generalized polygons, as well as incidence problems in the real or complex Euclidean spaces (eg. Szemerédi–Trotter theorem).
4
votes
Ree groups and Moufang octagons
Only having $k$ as subfield of $\ell$ is not sufficient (for both questions). The Ree groups (and the generalized octagons) are determined by a pair $(k, \theta)$, where $k$ is a field of characterist …
- 6,614
10
votes
Accepted
Which finite projective planes can have a symmetric incidence matrix?
The key word here is "polarity". A polarity of a projective plane with point set $P$ and line set $L$ is a map $\pi$ from $P \cup L$ to itself mapping points to lines and lines to points, such that $\ …
- 6,614
6
votes
Synthetic projective lines
Following up on Matthias Wendt's comment, the language of Moufang sets is indeed a suitable axiomatic approach to (generalizations of) projective lines.
Formally speaking, a Moufang set is a set $X$ …
- 6,614
9
votes
Accepted
What is the automorphism group of this geometry?
Your geometry has the property that each of its rank 2 restrictions is a Fano plane. In particular, the type-preserving automorphism group (let's call it $G$) is a subgroup of the automorphism group o …
- 6,614