Finite linear spaces with flag-transitive groups

DOI10.1016/0097-3165(88)90056-8zbMath0658.20001OpenAlexW1971802219MaRDI QIDQ1111693

Jean Doyen, Francis Buekenhout, Anne Delandtsheer

Publication date: 1988

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0097-3165(88)90056-8

zbMATH Keywords

primitive permutation groupssimple typefinite linear spacesincidence structureO'Nan-Scott theoremflag-transitive automorphism group2-(v,k,1)-designaffine typeflag-transitive finite linear spaces

Mathematics Subject Classification ID

Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Other designs, configurations (05B30) Combinatorial aspects of finite geometries (05B25) Combinatorial structures in finite projective spaces (51E20) Primitive groups (20B15) General theory for finite permutation groups (20B05)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• 2-transitive and antiflag transitive collineation groups of finite projective spaces
• On finite line transitive affine planes
• Transitivity on ordered pairs of lines in finite linear spaces
• Zweifach transitive, auflösbare Permutationsgruppen
• On perspectivities of finite projective planes
• On projective and affine planes with transitive collineation groups
• Some characterizations of finite projective spaces
• Geometric ABA-groups
• Steinersche Tripelsysteme mit fahnentransitiver Kollineationsgruppe
• The classification of the translation planes of order 16. I
• Steiner triple systems with doubly transitive automorphism groups: A corollary to the classification theorem for finite simple groups
• Block transitive automorphism groups of designs
• Homogeneous designs and geometric lattices
• Subgroups of prime power index in a simple group
• Flag-transitive projective planes
• Fahnentransitive Automorphismengruppen von Blockplänen. (Flag transitive automorphism groups of block designs.)
• Steiner triple systems with a doubly transitive automorphism group
• Flag-transitive finite simple groups
• Transitive linear groups and linear groups which contain irreducible subgroups of prime order. II
• Das kleinste Ree-Unital. (The smallest Ree-unital)
• 3/2-transitive permutation groups and designs
• A geometric consequence of the classification of finite doubly transitive groups
• Primitive permutation groups of odd degree, and an application to finite projective planes
• Flag-transitivity and primitivity
• Line-primitive groups of small rank
• Construction of two-dimensional flag-transitive planes
• Doubly homogeneous \(2\text{-}(v,k,1)\) designs
• Most block-transitive t-designs are point-primitive
• Ovoides et groupes de Suzuki
• Groups acting flag-transitively on designs
• The translation planes of order twenty-five
• Transitive linear groups and linear groups which contain irreducible subgroups of prime order
• Steiner triple systems with block-transitive automorphism groups
• Plane geometries associated with certain 2-transitive groups
• Fahnentransitive Ebenen gerader Ordnung
• A class of Frobenius regular groups
• Inductive subgroups of flag transitive groups
• Solvable, flag-transitive, rank 3 collineation groups
• Fahnentransitive Ebenen ungerader Ordnung
• Note on a consequence for affine groups of the classification theorem for finite simple groups
• Unitary block designs
• Solvability of groups of odd order
• On finite affine line transitive planes
• Scharf fahnentransitive endliche affine Räume
• Fahnenhomogene Quadrupelsysteme
• Some remarks concerning the Ree groups of type \((G_2)\)
• Solvable flag transitive affine groups
• Über projektive Ebenen, in denen jede Fahne von einer nicht-trivialen Elation invariant gelassen wird
• Finite affine planes with collineation groups primitive on the points
• Eine nicht-desarguesche zweifach transitive affine Ebene der Ordnung 27
• Finite affine planes of rank three are translation planes
• Über Translationsebenen mit Kollineationsgruppen, die die Punkte der ausgezeichneten Geraden zweifach transitiv permutieren
• Automorphism groups of designs
• A characterization of the Lüneburg planes
• Automorphisms of unitary block designs
• Finite translation planes with collineation groups doubly transitive on the points at infinity
• Line-transitive collineation groups of finite projective spaces
• Scharf transitive und scharf fahnentransitive Kollineationsgruppen
• Über nicht-Desarguessche Ebenen mit transitiver Translationsgruppe
• Projektive Ebenen über Fastkörpern
• A Class of Flag Transitive Planes
• Uniqueness of the Projective Plane of Order Eight
• On the Construction of Sets of Mutually Orthogonal Latin Squares and the Falsity of a Conjecture of Euler
• An exponential number of generalized Kerdock codes
• Spreads, Translation Planes and Kerdock Sets. II
• Finite Permutation Groups and Finite Simple Groups
• The Structure of Certain Triple Systems
• A New Flag Transitive Affine Plane of Order 27
• STEINER TRIPLE SYSTEMS WITH GEOMETRIC MINIMALLY GENERATED SUBSYSTEMS
• Flag-Transitive Planes of Even Order
• The construction of finite regular hyperbolic planes from inversive planes of even order
• On a Method of Construction of Partial Geometries and Partial Bolyai- Lobachevsky Planes
• On 2-Designs Whose Group of Automorphisms is Transitive on the Ordered Pairs of Intersecting Lines
• The Flag-Transitive Collineation Groups of the Finite Desarguesian Affine Planes
• The Trigonometry of GF(2 ²ⁿ ) and Finite Hyperbolic Planes
• Projective Planes
• Polarities in finite projective planes
• On the orbits of collineation groups
• On finite affine planes of rank 3

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