Constructive Recognition of Special Linear Groups

arXiv (Cornell University)

Abstract

We introduce a new constructive recognition algorithm for finite special linear groups in their natural representation. Given a group $G$ generated by a set of $d\times d$ matrices over a finite field $\mathbb{F}_q$, known to be isomorphic to the special linear group $\mathrm{SL}(d,q)$, the algorithm computes a special generating set $S$ for $G$. These generators enable efficient computations with the input group, including solving the word problem. Implemented in the computer algebra system GAP, our algorithm outperforms existing state-of-the-art algorithms by a significant margin. A detailed complexity analysis of the algorithm will be presented in an upcoming publication.

Authors 4

1. Max Horn

   Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau

   Affiliation as printed

   RPTU Kaiserslautern -Landau , Germany

2. Alice Niemeyer Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University , Germany

3. Cheryl E. Praeger

   The University of Western Australia

   Affiliation as printed

   University of Western Australia , Australia

4. Daniel Rademacher Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University , Germany