ISSN:
1572-9192
Keywords:
near polygon
;
diagram geometry
;
affine embedding
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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 $$\{ v_p |p \in P\} $$ Then the subspace generated by the vectors $$v_1 = \Sigma _{p*1} v_p $$ , where l $$\in $$ 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1022471817341
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