Presentations on standard generators for classical groups

For each family of finite classical groups, and their associated simple quotients, we provide an explicit presentation on a specific generating set of size at most 8. Since there exist efficient algorithms to construct this generating set in any copy of the group, our presentations can be used to ve...

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Bibliographic Details
Published inJournal of algebra Vol. 545; pp. 324 - 389
Main Authors Leedham-Green, C.R., O'Brien, E.A.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.03.2020
Subjects
Classical groups
Computational group theory
Short presentations
Standard generators
Classical groups
Short presentations
Computational group theory
Standard generators
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Summary:For each family of finite classical groups, and their associated simple quotients, we provide an explicit presentation on a specific generating set of size at most 8. Since there exist efficient algorithms to construct this generating set in any copy of the group, our presentations can be used to verify claimed isomorphisms between representations of the classical group. The presentations are available in Magma.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2019.07.024