Flag-transitive automorphism groups of 2-designs with λ ≥ (r, λ)^2 and an application to symmetric designs

DOI10.26493/1855-3974.1165.105zbMath1400.05035OpenAlexW2755718116MaRDI QIDQ3174803

Shenglin Zhou, Xiaoqin Zhan

Publication date: 18 July 2018

Published in: Ars Mathematica Contemporanea (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.26493/1855-3974.1165.105

zbMATH Keywords

automorphism groupflag-transitiveprimitivity2-designs

Mathematics Subject Classification ID

Combinatorial aspects of block designs (05B05) Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Combinatorial aspects of finite geometries (05B25)

Related Items (12)

Flag-transitive \(2\text{-}(v,k,\lambda)\) designs with \(r>\lambda(k-3)\) ⋮ Alternating groups and flag-transitive non-symmetric \(2\)-\((v,k, \lambda )\) designs with \(\lambda \geq (r, \lambda )^2\) ⋮ Flag-transitive automorphism groups of 2-designs with λ ≥ (r,λ)2 and k odd ⋮ A note on flag-transitive automorphism groups of 2-designs with \(\lambda \geq (r,\lambda )^2\) ⋮ Reduction for flag‐transitive 2‐(v,k,λ) designs with (r,λ)=2 ⋮ Block‐transitive automorphism groups of 2‐(v,k,λ) $(v,k,\lambda )$ designs with (r,k)=1 $(r,k)=1$ ⋮ A classification of flag-transitive 2-designs with \(\lambda \geq (r,\lambda)^2\) and sporadic socle ⋮ A reduction for block-transitive triple systems ⋮ Reduction of flag-transitive automorphism groups of \(2\)-\((v,k, \lambda )\) designs with \((r - \lambda ,k)=1\) ⋮ On flag-transitive automorphism groups of symmetric designs ⋮ Flag-transitive \(2\)-\((v, k, \lambda)\) symmetric designs with \(\lambda \geq (k, \lambda)^2\) and alternating socle ⋮ A parametrisation for symmetric designs admitting a flag-transitive, point-primitive automorphism group with a product action

Cites Work

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• A classification of flag-transitive 2-designs with \(\lambda \geq (r,\lambda)^2\) and sporadic socle
• Linear spaces with flag-transitive automorphism groups
• Reduction for primitive flag-transitive \((v, k, 4)\)-symmetric designs
• Primitive permutation groups of odd degree, and an application to finite projective planes
• Flag transitive automorphism groups of 2-designs with \((r,\lambda)=1\)
• The classification of finite linear spaces with flag-transitive automorphism groups of affine type
• On primitivity and reduction for flag-transitive symmetric designs
• On finite linear spaces with almost simple flag-transitive automorphism groups
• Flag‐Transitive Point‐Primitive Symmetric (ν,κ,λ) Designs With λ at Most 100

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