Constructive Recognition of Special Linear Groups

2024/04/29 by Max Horn, Horn, Max, Alice Niemeyer +5
Mathematics · #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2404.18860

openalex publication_date 2024/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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× d matrices over a finite field \mathbbF_q, known to be isomorphic to the special linear group 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.

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