An L2-quotient algorithm for finitely presented groups on arbitrarily many generators

2014/02/27 by Sebastian Jambor, Jambor, Sebastian · 2 citations
Computer Science · Mathematics · #20F05 #Algebra over a field #Algorithm #Coding theory and cryptography #Computer science #Discrete mathematics #FOS: Mathematics #Finite Group Theory Research #Finitely-generated abelian group #Geometric and Algebraic Topology #Group (periodic table) #Group Theory (math.GR) #Mathematics #Physics #Pure mathematics #Quotient #math.GR #msc:20F05

paper · pdf · doi:10.48550/arxiv.1402.6788

published in arXiv (Cornell University) (Cornell University) · 21 pages

arxiv created 2014/02/27 · openalex publication_date 2014/02/27 · arxiv updated 2014/02/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We generalize the Plesken-Fabiańska L₂-quotient algorithm for finitely presented groups on two or three generators to allow an arbitrary number of generators. The main difficulty lies in a constructive description of the invariant ring of GL(2, K) on m copies of SL(2, K) by simultaneous conjugation. By giving this description, we generalize and simplify some of the known results in invariant theory. An implementation of the algorithm is available in the computer algebra system Magma.

Citations

• Determining Aschbacher classes using characters

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