Presentations on standard generators for classical groups

2018/11/02 by C. R. Leedham-Green, Leedham-Green, C. R., E. A. O’Brien +2 · 1 citation
Computer Science · Mathematics · #20G40 #Algebra over a field #Arithmetic #Classical group #Coding theory and cryptography #Computer science #Construct (python library) #FOS: Mathematics #Finite Group Theory Research #Generating set of a group #Geometric and Algebraic Topology #Geometry #Group (periodic table) #Group Theory (math.GR) #Lie group #Magma #Mathematics #Physics #Presentation (obstetrics) #Programming language #Pure mathematics #Quotient #Set (abstract data type) #Simple (philosophy) #Theoretical computer science #math.GR #msc:20G40

paper · pdf · doi:10.48550/arxiv.1811.00685

openalex publication_date 2018/11/02 · arxiv created 2019/07/26 · arxiv updated 2019/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

For each family of finite classical groups, and their associated simple quotients, we provide an explicit presentation on a specific generating set of size at most 8. Since there exist efficient algorithms to construct this generating set in any copy of the group, our presentations can be used to verify claimed isomorphisms between representations of the classical group. The presentations are available in Magma.

Cited by

• Determining unit groups and K₁ of finite rings

Related

• Presentations of finite simple groups: a computational approach
• Constructive homomorphisms for classical groups
• Presentations of finite simple groups: a quantitative approach
• Short presentations of finite simple groups
• The (2,3)-generation of the classical simple groups of dimension 6 and 7