Soft planes and groups

2024/08/21 by William M. Kantor, Kantor, William M.
Decision Sciences · Mathematics · #05E18 (Primary) 20B25 #51E15 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Fuzzy and Soft Set Theory #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2408.11923

openalex publication_date 2024/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Finite projective planes are constructed using groups that satisfy simple-looking conditions. The resulting projective planes include many known planes and possibly new ones, and are precisely those having a collineation group fixing a flag (∞,L_ ∞ ) and transitive on the flags (w,W ) with w∉ L_ ∞ and ∞∉ W.

Related

• Transitive projective planes
• Existence of Projective Planes
• Finite Projective Planes
• New necessary conditions for the existence of finite non-Desarguesian flag-transitive projective plane
• Transitive projective planes and insoluble groups