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On 2‐Designs Whose Group of Automorphisms is Transitive on the Ordered Pairs of Intersecting Lines
Author(s) -
Buekenhout F.
Publication year - 1972
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-5.4.663
Subject(s) - transitive relation , automorphism , citation , automorphism group , group (periodic table) , combinatorics , mathematics , computer science , library science , physics , quantum mechanics
THEOREM 1. Let G be a permutation group on a finite set S of v points. If a, b are distinct points then the set ab of all points fixed by the stabilizer Gab will be called aline. Assume that (i) G is 2-transitive on the points of S; (ii) the number k of points on the line ab satisfies 2 < k < v; (iii) Gab is transitive on the lines containing a and distinct from ab. Then S provided with the set of lines is an affine space AG(d, q) of dimension d^lon some field oforderq ^ 3 or Sis a projective space PG(d, 2) of dimension d ^ 2 and order 2.