Flag-transitive non-symmetric 2-designs with \((r,\lambda)=1\) and sporadic socle

DOI10.1007/S10623-015-0171-6zbMath1347.05019OpenAlexW2226061700MaRDI QIDQ329191

Shenglin Zhou, Xiaoqin Zhan

Publication date: 21 October 2016

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-015-0171-6

zbMATH Keywords

2-designflag-transitivesoclesporadic simple group

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)

A classification of flag-transitive block designs ⋮ Classification of the non-trivial \(2\)-\((v,k,\lambda)\) designs, with \((r,\lambda)=1\) and \(\lambda >1\), admitting a non-solvable flag-transitive automorphism group of affine type ⋮ Block designs with \(\gcd(r,\lambda)=1\) admitting flag-transitive automorphism groups ⋮ Flag-transitive block designs with prime replication number and almost simple groups ⋮ Flag-transitive block designs and finite simple exceptional groups of Lie type ⋮ Classification of the non-trivial \(2\)-\((k^2,k, \lambda )\) designs, with \(\lambda |k\), admitting a flag-transitive almost simple automorphism group ⋮ Flag-transitive quasi-residual designs with sporadic socle ⋮ A classification of flag-transitive \(2\)-\((k^2, k, \lambda)\) designs with \(\lambda\mid k\) ⋮ A classification of flag-transitive 2-designs with \(\lambda \geq (r,\lambda)^2\) and sporadic socle ⋮ Three dimensional projective special linear groups on 2-designs ⋮ Flag-transitive block designs and unitary groups ⋮ Non-symmetric 2-designs admitting a two-dimensional projective linear group

Uses Software

• GAP
• Magma

Cites Work

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• Flag-transitive \(2-(v,k,\lambda )\) symmetric designs with \((k,\lambda)=1\) and alternating socle
• Linear spaces with flag-transitive automorphism groups
• Flag-transitivity and primitivity
• Flag transitive automorphism groups of 2-designs with \((r,\lambda)=1\)
• The Magma algebra system. I: The user language
• Flag-transitive non-symmetric 2-designs with \((r,\lambda)=1\) and alternating socle
• Explicit representations of maximal subgroups of the Monster.
• Sporadic groups and automorphisms of linear spaces
• Flag‐Transitive 2‐ Symmetric Designs with Sporadic Socle

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