The nonexistence of certain generalized polygons

Feit, Walter; Higman, Graham

doi:10.1016/0021-8693(64)90028-6

Cited by 329 publications

(247 citation statements)

References 2 publications

Supporting

Mentioning

242

Contrasting

Unclassified

Order By: Relevance

“…A major result on finite generalized polygons is due to Feit & Higman [6] and states that for a finite generalized n-gon, n ≥ 3, of order (s, t), we always have either n = 3 (and then s = t), or n = 4 (and then s + t divides st(1 + st)), or n = 6 (and then st is a perfect square), or n = 8 (and then 2st is a perfect square), or n = 12 (and then 1 ∈ {s, t}). Each generalized n-gon S = (P, L, I) of order (s, s) gives rise to a unique generalized 2n-gon 2S = (P ∪ L, E) of order (1, s), called the double of S, where E is the set of flags of S (and a flag is an incident point-line pair).…”

Section: Notation and Main Resultsmentioning

confidence: 99%

On collineations and dualities of finite generalized polygons

2009

View full text Add to dashboard Cite

In this paper we generalize a result of Benson to all finite generalized polygons. In particular, given a collineation θ of a finite generalized polygon S, we obtain a relation between the parameters of S and, for various natural numbers i, the number of points x which are mapped to a point at distance i from x by θ. As a special case we consider generalized 2n-gons of order (1, t) and determine, in the generic case, the exact number of absolute points of a given duality of the underlying generalized n-gon of order t.

show abstract

Section: Notation and Main Resultsmentioning

confidence: 99%

On collineations and dualities of finite generalized polygons

2009

View full text Add to dashboard Cite

show abstract

“…Thus the length of the code is It is possible to construct longer codes from generalized N-gons, but it is known [12] that for N > 6 there are no N-gons with degree q + 1.…”

Section: Expander Graphs From Geometriesmentioning

confidence: 99%

The Minimum Distance of Graph Codes

Høholdt

Justesen

2011

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…(1) By [18, Lemma 1.3.6] condition (i) is equivalent to G being the incidence graph of a generalized m-gon. Since G is finite it then follows from the theorem of Feit and Higman [10] that m A f2; 3; 4; 6; 8g.…”

Section: Definitionmentioning

confidence: 99%