Journal article

Publication year: 1993

Pages: 375-381

Journal: Journal of Algebraic Combinatorics

Volume number: 2

Issue number: 4

ISSN: 0925-9899

Open access status: Bronze

DOI Link: https://doi.org/10.1023/A:1022471817341

Publisher: Springer

Abstract: 

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 is-an-element-of P}. Then the subspace generated by the vectors v(l) = SIGMA(p*l), v(p), where l is-an-element-of 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.

Harvard Citation style: CUYPERS, H. and MEIXNER, T. (1993) SOME EXTENSIONS AND EMBEDDINGS OF NEAR POLYGONS, Journal of Algebraic Combinatorics, 2(4), pp. 375-381. https://doi.org/10.1023/A:1022471817341

APA Citation style: CUYPERS, H., & MEIXNER, T. (1993). SOME EXTENSIONS AND EMBEDDINGS OF NEAR POLYGONS. Journal of Algebraic Combinatorics. 2(4), 375-381. https://doi.org/10.1023/A:1022471817341