Finite groups of matrices over quadratic number fields

2025/11/06 by Yurshevich, Daniil
Computer Science · Mathematics · #Cryptography and Residue Arithmetic #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2511.05621

openalex publication_date 2025/11/06 · openalex created_date 2025/11/12 · openalex updated_date 2026/07/28

Abstract

In this paper we give an algorithm to determine all finite matrix groups over a number field. Our algorithm is based on the representation theory of finite groups.

Citations

• Zeta function of some Kummer Calabi-Yau 3-folds
• Higher dimensional Calabi-Yau manifolds of Kummer type
• Bounds for the orders of the finite subgroups of G(k)
• On the Kummer construction
• Generalised Kummer constructions and Weil restrictions
• Orders of Finite Groups of Matrices
• Intermediate Jacobian and Some Arithmetic Properties of Kummer-surface-type CY 3-folds

Related

• Four Drafts of The Representation Theory of the Group of Infinite Matrices over Finite Fields
• Practical computation with linear groups over infinite domains
• An algorithm for determining the irreducible polynomials over finite fields
• Counting Elements on Full Matrix Groups over Finite Field with Prescribed Eigenvalues
• Reduction for characters of finite algebra groups