Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.18860 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909184196345856 |
|---|---|
| author | Horn, Max Niemeyer, Alice Praeger, Cheryl Rademacher, Daniel |
| author_facet | Horn, Max Niemeyer, Alice Praeger, Cheryl Rademacher, Daniel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18860 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Constructive Recognition of Special Linear Groups Horn, Max Niemeyer, Alice Praeger, Cheryl Rademacher, Daniel Group Theory 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. |
| title | Constructive Recognition of Special Linear Groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2404.18860 |