Doubly homogeneous 2-(v, k, 1) designs

Anne Delendtsheer; Jean Doyen; Johannes Siemons; Chiara Tamburini

doi:10.1016/0097-3165(86)90033-6

Doubly homogeneous 2-(v, k, 1) designs

Anne Delendtsheer, Jean Doyen, Johannes Siemons, Chiara Tamburini

Research output: Contribution to journal › Article › peer-review

25 Citations (Scopus)

Abstract

If D is a 2-(v, k, 1) design admitting a group G of automorphisms which acts doubly homogeneously but not doubly transitively on the points, we prove that v = pⁿ for some prime p ≡ 3 (mod 4), n is odd and
1. (1)D is an affine space over a subfield of GF(pⁿ) or

2. (2)D is a Netto system, k = 3 and p ≡ 7 (mod 12).

Original language	English
Pages (from-to)	140-145
Number of pages	6
Journal	Journal of Combinatorial Theory, Series A
Volume	43
Issue number	1
DOIs	https://doi.org/10.1016/0097-3165(86)90033-6
Publication status	Published - 1986

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Cite this

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title = "Doubly homogeneous 2-(v, k, 1) designs",

abstract = "If D is a 2-(v, k, 1) design admitting a group G of automorphisms which acts doubly homogeneously but not doubly transitively on the points, we prove that v = pn for some prime p ≡ 3 (mod 4), n is odd and1. (1)D is an affine space over a subfield of GF(pn) or2. (2)D is a Netto system, k = 3 and p ≡ 7 (mod 12).",

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T1 - Doubly homogeneous 2-(v, k, 1) designs

AU - Delendtsheer, Anne

AU - Doyen, Jean

AU - Siemons, Johannes

AU - Tamburini, Chiara

PY - 1986

Y1 - 1986

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AB - If D is a 2-(v, k, 1) design admitting a group G of automorphisms which acts doubly homogeneously but not doubly transitively on the points, we prove that v = pn for some prime p ≡ 3 (mod 4), n is odd and1. (1)D is an affine space over a subfield of GF(pn) or2. (2)D is a Netto system, k = 3 and p ≡ 7 (mod 12).

U2 - 10.1016/0097-3165(86)90033-6

DO - 10.1016/0097-3165(86)90033-6

M3 - Article

VL - 43

SP - 140

EP - 145

JO - Journal of Combinatorial Theory, Series A

JF - Journal of Combinatorial Theory, Series A

SN - 0097-3165

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