Constructive Recognition of Special Linear Groups

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 Fq, 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.