On the quasi group of a cubic surface over a finite field

2011/02/07 by Andreas-Stephan Elsenhans, Elsenhans, Andreas-Stephan, Jörg Jahnel +1
Mathematics · #11G25 #14G15 #14J20 #14J26 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1102.1278

openalex publication_date 2011/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct nontrivial homomorphisms from the quasi group of some cubic surfaces over \bbF _p into a group. We show experimentally that the homomorphisms constructed are the only possible ones and that there are no nontrivial homomorphisms in the other cases. Thereby, we follow the classification of cubic surfaces, due to A. Cayley.

Related

• Groups acting on cubic surfaces in characteristic zero
• Automorphisms of cubic surfaces without points
• Automorphisms of cubic surfaces in positive characteristic
• The most symmetric smooth cubic surface
• Cubic surfaces with infinite, discrete automorphism group