Linear spaces with flag-transitive automorphism groups
From MaRDI portal
Publication:919612
DOI10.1007/BF00181466zbMath0707.51017OpenAlexW1972018650MaRDI QIDQ919612
Jan Saxl, Martin W. Liebeck, Anne Delandtsheer, Jean Doyen, Francis Buekenhout, Peter B. Kleidman
Publication date: 1990
Published in: Geometriae Dedicata (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf00181466
Other finite linear geometries (51E26) Homomorphism, automorphism and dualities in linear incidence geometry (51A10)
Related Items
3-Homogeneous groups and flag-transitive 6-(v, k, 3) designs ⋮ Flag-transitive quasi-symmetric designs with block intersection numbers 0 and 2 ⋮ Classifications of finite highly transitive dimensional linear spaces ⋮ 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 \(F_4(q)\) ⋮ 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 ⋮ On block-transitive 2--(\(v\), 4, 1) designs ⋮ Flag-transitive automorphism groups of 2-designs with λ ≥ (r, λ)^2 and an application to symmetric designs ⋮ Unnamed Item ⋮ A survey of minimal clones ⋮ Classification of flag-transitive point-primitive non-symmetric 2-\((v, k, \lambda)\) designs with \(v < 100\) ⋮ A characterization of truncated projective geometries as flag-transitive \((PG^{*}.PG)\)-geometries ⋮ The flag-transitive symmetric designs with 45 points, blocks of size 12, and 3 blocks on every point pair ⋮ Flag-transitive non-symmetric 2-designs with \((r,\lambda)=1\) and sporadic socle ⋮ Block designs with \(\gcd(r,\lambda)=1\) admitting flag-transitive automorphism groups ⋮ On maximal closed subsets in association schemes ⋮ Almost simple groups with socle \(^{3} D_{4}( q )\) act on finite linear spaces ⋮ Finite flag-transitive affine planes with a solvable automorphism group ⋮ A classification of line-transitive maximal (v,k)-arcs in finite projective planes ⋮ Reduction for primitive flag-transitive symmetric \(2\)-\(( v , k , \lambda )\) designs with \(\lambda\) prime ⋮ Flag-transitive block designs with prime replication number and almost simple groups ⋮ \(s\)-flag-transitive designs for \(s \geq 4\) ⋮ Symmetric designs admitting flag-transitive and point-primitive almost simple automorphism groups of Lie type ⋮ The Chevalley groups \(G_2(q)\) with \(q\) odd and 2-\((v,k,1)\) designs ⋮ Alternating groups and point‐primitive linear spaces with number of points being squarefree ⋮ Classification of the non-trivial \(2\)-\((k^2,k, \lambda )\) designs, with \(\lambda |k\), admitting a flag-transitive almost simple automorphism group ⋮ Block-transitive \(3\)-\((v, k, 1)\) designs associated with alternating groups ⋮ A construction of one-dimensional affine flag-transitive linear spaces ⋮ Block‐transitive automorphism groups of 2‐(v,k,λ) $(v,k,\lambda )$ designs with (r,k)=1 $(r,k)=1$ ⋮ The asymptotic behavior of Chern-Simons Higgs model on a compact Riemann surface with boundary ⋮ Flag-transitive 2-(v,k,λ) designs with λ prime and alternating socle ⋮ New families of flag-transitive linear spaces ⋮ Finite linear spaces admitting a two-dimensional projective linear group ⋮ More translation planes and semifields from Dembowski-Ostrom polynomials ⋮ Finite linear spaces admitting a projective group \(\text{PSU}(3,q)\) with \(q\) even ⋮ The \(2\)-\((v,11,1)\) designs with unsolvable block transitive automorphism ⋮ A classification of flag-transitive \(2\)-\((k^2, k, \lambda)\) designs with \(\lambda\mid k\) ⋮ Reduction for primitive flag-transitive nonsymmetric 2-(v,k,4) designs ⋮ Finite linear spaces admitting a Ree simple group. ⋮ Quadratic extensions of flag-transitive planes ⋮ Some infinite families of 2‐designs from PG (n, q) ⋮ Finite flag-transitive semiovals ⋮ On the automorphisms of \(2 -(v, k, 1)\) designs ⋮ Some properties of graphs constructed from 2-designs ⋮ The classification of flag-transitive Steiner 4-designs ⋮ Triple factorisations of the general linear group and their associated geometries. ⋮ A census of highly symmetric combinatorial designs ⋮ Dimensional linear spaces whose automorphism group is (line, hyperplane)- flag transitive ⋮ Flag-transitive affine planes of order at most 125 ⋮ 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 ⋮ Three dimensional projective special linear groups on 2-designs ⋮ Classification of point-primitive linear spaces with \(2pq\) points ⋮ Line-primitive \(2\)-\((v,k,1)\) designs with \(k/(k,v)\leq 10\) ⋮ Solvable block-transitive automorphism groups of \(2\)-\((v,k,1)\) designs ⋮ The non-solvable rank 3 affine planes ⋮ On the Cameron-Praeger conjecture ⋮ On flag-transitive \(2\)-\((v,k,2)\) designs ⋮ Pairwise transitive 2-designs ⋮ Extremely primitive groups and linear spaces ⋮ Classification of flag-transitive Steiner quadruple systems ⋮ \(2\)-\((v, k, 1)\) 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 ⋮ Affine planes admitting a collineation group with a transitive action on the line at infinity ⋮ Almost simple groups with socle \(\text{Ree}(q)\) acting on finite linear spaces. ⋮ Suzuki groups and 2-\((v,k,1)\) designs ⋮ Flag-transitive \(2\)-\((\upsilon , 5, \lambda )\) designs with sporadic socle ⋮ Automorphism groups of linear spaces and their parabolic subgroups ⋮ The existence and construction of a family of block-transitive 2-(\(v\),6,1)designs ⋮ Non-symmetric 2-designs admitting a two-dimensional projective linear group ⋮ 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 ⋮ Partial linear spaces with a rank 3 affine primitive group of automorphisms ⋮ An arithmetic reduction of finite rank 3 geometries with linear spaces as plane residues and with dual linear spaces as point residues ⋮ Point-primitive linear spaces with number of points being a product of two primes ⋮ The mathematics of Donald Gordon Higman ⋮ The classification of finite linear spaces with flag-transitive automorphism groups of affine type ⋮ Flag-Transitive Point-Primitive Automorphism Groups of Nonsymmetric 2−(v,k,2) Designs ⋮ Blocking sets with flag transitive collineation groups ⋮ Finite line-transitive linear spaces: theory and search strategies ⋮ Flag-transitive \(4\)-\((v, k, 3)\) designs and \(\mathrm{PSL}(2, q)\) groups ⋮ On flag-transitive automorphism groups of 2-designs ⋮ Homogeneity in finite ordered sets ⋮ On finite linear spaces with almost simple flag-transitive automorphism groups ⋮ A generalisation of Johnson graphs with an application to triple factorisations ⋮ Solvable line-transitive automorphism groups of finite linear spaces ⋮ Homogeneous coherent configurations from spherical buildings and other edge-coloured graphs
