Translation Partial Geometries

Clerck, Frank De; Gevaert, Hans; Thas, J. A.

doi:10.1016/s0167-5060(08)70231-0

Cited by 8 publications

(10 citation statements)

References 10 publications

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“…Under a small restriction this is indeed possible. The basic ideas for the proof of this observation are taken from De Winter [4] (see also De Clerck et al [2]). …”

Section: Proof Of the Main Theorem Corollariesmentioning

confidence: 97%

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Generalized Quadrangles with an Abelian Singer Group

Winter

Thas

2006

Des Codes Crypt

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“…Under a small restriction this is indeed possible. The basic ideas for the proof of this observation are taken from De Winter [4] (see also De Clerck et al [2]). …”

Section: Proof Of the Main Theorem Corollariesmentioning

confidence: 97%

“…In the paper [2] translation partial geometries are introduced, and thoroughly studied. These are partial geometries with parameters (s, t, α) admitting a regular abelian automorphism group, so that each line orbit is a normal spread and t = α(s + 2).…”

Section: Introductionmentioning

confidence: 99%

Generalized Quadrangles with an Abelian Singer Group

Winter

Thas

2006

Des Codes Crypt

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“…R is called α-geometric [1] (see also [5]) if for any two elements and of R the (2m + 1)-dimensional subspace , contains precisely α + 1 elements of R. If m = 0, then this property always holds since R intersects every line in 0, 1 or α + 1 points. Now let m > 0 and suppose that an element of R intersects the (2m + 1)-dimensional subspace , , with , ∈ R. Choose a point z ∈ ∩ , , and consider the (m + 1)-dimensional subspace z, .…”

Section: A Characterisationmentioning

confidence: 99%

Distance-Regular (0,α)-Reguli

et al. 2006

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We introduce distance-regular (0, α)-reguli and show that they give rise to (0, α)-geometries with a distance-regular point graph. This generalises the SPG-reguli of Thas [14] and the strongly regular (α, β)-reguli of Hamilton and Mathon [9], which yield semipartial geometries and strongly regular (α, β)-geometries, respectively. We describe two infinite classes of examples, one of which is a generalisation of the well-known semipartial geometry T * n (B) arising from a Baer subspace PG(n, q) in PG(n, q 2 ).

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“…In [7] a theory of translation partial geometries was introduced as follows. Let G be an abelian group of order (s + 1) 3 (s 1) and let J = {A 0 , .…”

Section: A Special Propertymentioning

confidence: 99%

“…SPG-reguli were introduced by Thas [15]. An SPG-regulus R is called -geometric if the (2m+1)-space generated by any two distinct elements of R contains exactly + 1 elements of R (see [7]). …”

Section: Introduction and Basic Notionsmentioning

confidence: 99%

Elation and translation semipartial geometries

Winter

2004

Journal of Combinatorial Theory, Series A

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We introduce a theory of elation and translation semipartial geometries (SPG). Starting from an SPG-family (G, J ), i.e. a not necessarily abelian group G and a collection of subgroups J = {S 0 , . . . , S t } satisfying some extra condition, we construct a semipartial geometry S as a coset geometry. We show that there are strong relations between the theory of these geometries and that of elation and translation generalized quadrangles. We show for example that the theory of translation semipartial geometries is in fact almost equivalent to the study of SPG-reguli in PG(n, q). We introduce a special class of automorphisms, called parallelisms, for these geometries and examine the structure of fixed points and lines under these automorphisms. In the case that G is abelian we show that in almost all cases Aut(S) A L(n + 2, q) for certain n and q.

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Translation Partial Geometries

Cited by 8 publications

References 10 publications

Generalized Quadrangles with an Abelian Singer Group

Generalized Quadrangles with an Abelian Singer Group

Distance-Regular (0,α)-Reguli

Elation and translation semipartial geometries

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