Sporadic groups and automorphisms of linear spaces

DOI<link itemprop=identifier href="https://doi.org/10.1002/1520-6610(2000)8:5<353::AID-JCD5>3.0.CO;2-G" /><353::AID-JCD5>3.0.CO;2-G 10.1002/1520-6610(2000)8:5<353::AID-JCD5>3.0.CO;2-GzbMath0974.20002OpenAlexW2015397548MaRDI QIDQ4508626

Federica Spiezia, Alan R. Camina

Publication date: 20 June 2001

Full work available at URL: https://doi.org/10.1002/1520-6610(2000)8:5<353::aid-jcd5>3.0.co;2-g

zbMATH Keywords

flag-transitive automorphism groupssoclesfinite linear spacesline transitive automorphism groupspoint transitive automorphism groups

Mathematics Subject Classification ID

Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Other finite linear geometries (51E26) Homomorphism, automorphism and dualities in linear incidence geometry (51A10)

Related Items (25)

Block-transitive 2-\((v, k, 1)\) designs and the twisted simple groups \({}^2 E_6(q)\) ⋮ Block-transitive \(2\)-\((v, k, 1)\) designs and the Chevalley groups \(F_4(q)\) ⋮ Flag-transitive non-symmetric 2-designs with \((r,\lambda)=1\) and sporadic socle ⋮ Unsolvable block transitive automorphism groups of \(2\)-\((v,5,1)\) designs ⋮ Almost simple groups with socle \(^{3} D_{4}( q )\) act on finite linear spaces ⋮ The Chevalley groups \(G_2(q)\) with \(q\) odd and 2-\((v,k,1)\) designs ⋮ Flag-transitive quasi-residual designs with sporadic socle ⋮ Block-transitive \(3\)-\((v, k, 1)\) designs associated with alternating groups ⋮ On symmetric designs with flag‐transitive and point‐quasiprimitive automorphism groups ⋮ Finite linear spaces admitting a two-dimensional projective linear group ⋮ Extremely line-primitive automorphism groups of finite linear spaces ⋮ Finite linear spaces admitting a projective group \(\text{PSU}(3,q)\) with \(q\) even ⋮ Finite linear spaces admitting a Ree simple group. ⋮ Automorphisms of linear spaces and groups \(^2E_6(q)\) ⋮ On the automorphisms of \(2 -(v, k, 1)\) designs ⋮ 2-\((v,k,1)\) designs with a point-primitive rank 3 automorphism group of affine type ⋮ A classification of flag-transitive 2-designs with \(\lambda \geq (r,\lambda)^2\) and sporadic socle ⋮ \(2\)-\((v, k, 1)\) designs admitting automorphism groups with socle \(\mathrm{Sz}(q)\) ⋮ 2‐(v,k,1) Designs Admitting a Primitive Rank 3 Automorphism Group of Affine Type: The Extraspecial and the Exceptional Classes ⋮ Almost simple groups with socle \(\text{Ree}(q)\) acting on finite linear spaces. ⋮ Unsolvable block transitive automorphism groups of \(2-(v,k,1)(k=6,7,8,9)\) designs ⋮ Point-primitive linear spaces with number of points being a product of two primes ⋮ Finite line-transitive linear spaces: theory and search strategies ⋮ Flag‐Transitive 2‐ Symmetric Designs with Sporadic Socle ⋮ Finite projective planes admitting a projective linear group \(\operatorname{PSL}(2, q)\)

Uses Software

• GAP
• Magma

Cites Work

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• Steiner triple systems with doubly transitive automorphism groups: A corollary to the classification theorem for finite simple groups
• Block transitive automorphism groups of designs
• Primitive permutation groups of odd degree, and an application to finite projective planes
• Most block-transitive t-designs are point-primitive
• Block transitive automorphism groups of 2-(v,k,1) block designs
• Steiner triple systems with block-transitive automorphism groups
• On block-transitive 2--(\(v\), 4, 1) designs
• The Socle of Automorphism Groups of Linear Spaces
• On the orbits of collineation groups

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