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• W2071032904 abstract "Let S be a translation generalized quadrangle (TGQ) of order ( s , s 2 ) , s > 1 and s odd, with a good line L . Then there are precisely s 3 + s 2 subquadrangles of order s containing L . When S is isomorphic to the classical generalized quadrangle Q ( 5 , s ) , that is, the generalized quadrangle arising from a nonsingular quadric of Witt index 2 in PG ( 5 , s ) , then the stabilizer of L in the automorphism group of S acts transitively on these subquadrangles. It has been an open question for some time whether this is also the case when S is non-classical. In this paper, we prove that a transitive action on these subquadrangles forces S to be isomorphic to Q ( 5 , s ) . The latter theorem is a corollary of a stronger result that will be obtained, using the proof of a ‘ Stabilizer Lemma ’, which allows us to interpret collineations of a semifield flock TGQ (in odd characteristic) in the associated good TGQ. Other applications will be obtained." @default.
• W2071032904 created "2016-06-24" @default.
• W2071032904 creator A5012344209 @default.
• W2071032904 date "2007-01-01" @default.
• W2071032904 modified "2023-09-24" @default.
• W2071032904 title "A stabilizer lemma for translation generalized quadrangles" @default.
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• W2071032904 doi "https://doi.org/10.1016/j.ejc.2005.10.008" @default.
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