Ealy's conjecture in odd characteristic

2025/11/26 by Feng, Tao, Thas, Koen
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.21791

Abstract

We solve Ealy's conjecture from 1977 by showing that for each odd prime p, a finite generalized quadrangle each point of which admits a central symmetry of order p, is either a classical symplectic quadrangle in dimension 3, or a Hermitian quadrangle in dimension 3 or 4. As a byproduct, we vastly generalize the aforementioned result by determining the finite generalized quadrangles whose every point admits at least one nontrivial central symmetry.

Citations

• Generalized Quadrangles Of Order (s, s²). IV. Translations, Moufang And Fong-Seitz
• A classification of finite locally 2-transitive generalized quadrangles
• Simple groups, product actions, and generalised quadrangles
• A classification of finite antiflag-transitive generalized quadrangles
• Large subgroups of simple groups
• On the Orders of Maximal Subgroups of the Finite Exceptional Groups of Lie Type
• The local structure of finite groups of characteristic 2 type

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• A Survey of the Hodge Conjecture for Abelian Varieties