Geodesic
Some extensions and embeddings of near polygons
Journal of Algebraic Combinatorics, Tome 2 (1993) no. 4, pp. 375-381.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let ( P, L, *) be a near polygon having $s + 1$ points per line, $s > 1$, and suppose $k$ is a field. Let $V _{k}$ be the $k$-vector space with basis ${ v _{ p} | p$ Ĩ $P}$ { v_p |p $\in P$} Then the subspace generated by the vectors $v _{1} = S _{ p*1} v _{ p} v_1 = \Sigma $_p*1 v_p , where $l$ Ĩ $\in L$, has codimension at least 2 in $V _{k}$. This observation is used in two ways. First we derive the existence of certain diagram geometries with flag transitive automorphism group, and secondly, we show that any finite near polygon with 3 points per line can be embedded in an affine $GF(3)$-space.
Keywords: near polygon, diagram geometry, affine embedding 
@article{JAC_1993__2_4_a3,
     author = {Cuypers, Hans and Meixner, Thomas},
     title = {Some extensions and embeddings of near polygons},
     journal = {Journal of Algebraic Combinatorics},
     pages = {375--381},
     publisher = {mathdoc},
     volume = {2},
     number = {4},
     year = {1993},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_1993__2_4_a3/}
}
TY  - JOUR
AU  - Cuypers, Hans
AU  - Meixner, Thomas
TI  - Some extensions and embeddings of near polygons
JO  - Journal of Algebraic Combinatorics
PY  - 1993
SP  - 375
EP  - 381
VL  - 2
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_1993__2_4_a3/
LA  - en
ID  - JAC_1993__2_4_a3
ER  - 
%0 Journal Article
%A Cuypers, Hans
%A Meixner, Thomas
%T Some extensions and embeddings of near polygons
%J Journal of Algebraic Combinatorics
%D 1993
%P 375-381
%V 2
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_1993__2_4_a3/
%G en
%F JAC_1993__2_4_a3
Cuypers, Hans; Meixner, Thomas. Some extensions and embeddings of near polygons. Journal of Algebraic Combinatorics, Tome 2 (1993) no. 4, pp. 375-381. http://geodesic.mathdoc.fr/item/JAC_1993__2_4_a3/