Algorithms determining finite simple images of finitely presented groups
We address the question: for which collections of finite simple groups does there exist an algorithm that determines the images of an arbitrary finitely presented group that lie in the collection? We prove both positive and negative results. For a collection of finite simple groups that contains inf...
| मुख्य लेखकों: | , , , |
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| स्वरूप: | Journal article |
| प्रकाशित: |
Springer Verlag
2019
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| _version_ | 1826317534276616192 |
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| author | Bridson, M Evans, D Liebeck, M Segal, D |
| author_facet | Bridson, M Evans, D Liebeck, M Segal, D |
| author_sort | Bridson, M |
| collection | OXFORD |
| description | We address the question: for which collections of finite simple groups does there exist an algorithm that determines the images of an arbitrary finitely presented group that lie in the collection? We prove both positive and negative results. For a collection of finite simple groups that contains infinitely many alternating groups, or contains classical groups of unbounded dimensions, we prove that there is no such algorithm. On the other hand, for families of simple groups of Lie type of bounded rank, we obtain positive results. For example, for any fixed untwisted Lie type X there is an algorithm that determines whether or not any given finitely presented group has simple images of the form X(q) for infinitely many q, and if there are finitely many, the algorithm determines them. |
| first_indexed | 2024-03-07T01:25:19Z |
| format | Journal article |
| id | oxford-uuid:91c5fc8a-ddeb-4824-8e27-8a2107f363f2 |
| institution | University of Oxford |
| last_indexed | 2025-03-11T16:55:26Z |
| publishDate | 2019 |
| publisher | Springer Verlag |
| record_format | dspace |
| spelling | oxford-uuid:91c5fc8a-ddeb-4824-8e27-8a2107f363f22025-02-21T09:46:25ZAlgorithms determining finite simple images of finitely presented groupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:91c5fc8a-ddeb-4824-8e27-8a2107f363f2Symplectic Elements at OxfordSpringer Verlag2019Bridson, MEvans, DLiebeck, MSegal, DWe address the question: for which collections of finite simple groups does there exist an algorithm that determines the images of an arbitrary finitely presented group that lie in the collection? We prove both positive and negative results. For a collection of finite simple groups that contains infinitely many alternating groups, or contains classical groups of unbounded dimensions, we prove that there is no such algorithm. On the other hand, for families of simple groups of Lie type of bounded rank, we obtain positive results. For example, for any fixed untwisted Lie type X there is an algorithm that determines whether or not any given finitely presented group has simple images of the form X(q) for infinitely many q, and if there are finitely many, the algorithm determines them. |
| spellingShingle | Bridson, M Evans, D Liebeck, M Segal, D Algorithms determining finite simple images of finitely presented groups |
| title | Algorithms determining finite simple images of finitely presented groups |
| title_full | Algorithms determining finite simple images of finitely presented groups |
| title_fullStr | Algorithms determining finite simple images of finitely presented groups |
| title_full_unstemmed | Algorithms determining finite simple images of finitely presented groups |
| title_short | Algorithms determining finite simple images of finitely presented groups |
| title_sort | algorithms determining finite simple images of finitely presented groups |
| work_keys_str_mv | AT bridsonm algorithmsdeterminingfinitesimpleimagesoffinitelypresentedgroups AT evansd algorithmsdeterminingfinitesimpleimagesoffinitelypresentedgroups AT liebeckm algorithmsdeterminingfinitesimpleimagesoffinitelypresentedgroups AT segald algorithmsdeterminingfinitesimpleimagesoffinitelypresentedgroups |