Automorphisms and isomorphisms of symmetric and affine designs

DOI10.1023/A:1022416002358zbMath0807.05005MaRDI QIDQ1330171

William M. Kantor

Publication date: 23 August 1994

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

zbMATH Keywords

permutationsautomorphism groupssymmetric designsprojective spacesSteiner triple systemsaffine designsrepresentation of finite groups

Mathematics Subject Classification ID

Combinatorial aspects of block designs (05B05) Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Combinatorial structures in finite projective spaces (51E20)

Related Items (20)

Recent results on designs with classical parameters ⋮ Twisted McFarland and Spence designs and their automorphisms ⋮ Arbitrary groups as two-point stabilisers of symmetric groups acting on partitions ⋮ Variations on the Dembowski-Wagner theorem. ⋮ On the number of designs with affine parameters ⋮ On the characterisation of AG\((n,q)\) by its parameters as a nearly triply regular design ⋮ Bounds on the number of Hadamard designs of even order ⋮ The number of designs with geometric parameters grows exponentially ⋮ Designs having the parameters of projective and affine spaces ⋮ Affine designs and linear orthogonal arrays ⋮ Exponential bounds on the number of designs with affine parameters ⋮ Structure and automorphism groups of Hadamard designs ⋮ Distorting symmetric designs ⋮ Polarities, quasi-symmetric designs, and Hamada's conjecture ⋮ Correction to: “Exponential bounds on the number of designs with affine parameters” ⋮ Universal families of permutation groups. ⋮ Automorphism groups of designs with \(\lambda = 1\) ⋮ On generalized Hadamard matrices of minimum rank ⋮ Bounds on the number of affine, symmetric, and Hadamard designs and matrices ⋮ Symmetric designs form the \(G_2(q)\) generalized hexagons

Cites Work

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• Some characterizations of finite projective spaces
• The number of designs with classical parameters grows exponentially
• Two remarks on affine designs with classical parameters
• Symplectic groups, symmetric designs, and line ovals
• Dimension and embedding theorems for geometric lattices
• Nonisomorphic Hadamard designs
• On the groups of automorphisms of Steiner triple and quadruple systems
• Hadamard designs with no non-trivial automorphisms
• A Combinatorial Problem

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