On finite generalized quadrangles with PSL(2,q) as an automorphism group

Let S be a finite thick generalized quadrangle, and suppose that G is an automorphism group of S . If G acts primitively on both the points and lines of S , then it is known that G must be almost simple. In this paper, we show that if the socle of G is PSL ( 2 , q ) with q ≥ 4 , then q = 9 and S is...

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Bibliographic Details
Published in:Designs, codes, and cryptography Vol. 91; no. 6; pp. 2347 - 2364
Main Authors: Feng, Tao, Lu, Jianbing
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2023
Springer Nature B.V
Subjects:
Automorphisms
Coding and Information Theory
Computer Science
Cryptology
Discrete Mathematics in Computer Science
Geometry
Inequality
Polygons
20B25
Point-primitive
Generalized quadrangle
Automorphism group
Projective linear group
05B25
Line-primitive
20B15
ISSN:0925-1022, 1573-7586
Online Access:Get full text
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Summary:Let S be a finite thick generalized quadrangle, and suppose that G is an automorphism group of S . If G acts primitively on both the points and lines of S , then it is known that G must be almost simple. In this paper, we show that if the socle of G is PSL ( 2 , q ) with q ≥ 4 , then q = 9 and S is the unique generalized quadrangle of order 2.
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ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-023-01203-x