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The Classification of Finite Generalized Quadrangles Admitting a Group Acting Transitively on Ordered Pentagons
Author(s) -
Thas J. A.,
Van Maldeghem H.
Publication year - 1995
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/51.2.209
Subject(s) - quadrangle , mathematics , combinatorics , group (periodic table) , degenerate energy levels , automorphism , set (abstract data type) , simple (philosophy) , simple group , finite set , computer science , physics , mathematical analysis , geology , philosophy , epistemology , quantum mechanics , programming language , geomorphology
Let be a thick generalized quadrangle and let G be a group of automorphisms of . If G acts transitively on the set of non‐degenerate ordered pentagons, then is one of the classical generalized quadrangles W ( q ), Q (4, q ), Q (5, q ) or H (3, q 2 ). The possibilities for G in each case are determined. We do not use the classification of the finite simple groups (from which this result also follows).