Two generators for the general linear groups over finite fields

DOI10.1080/03081088908817916zbMath0702.20050OpenAlexW2063596751MaRDI QIDQ3480275

William C. Waterhouse

Publication date: 1989

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081088908817916

zbMATH Keywords

general linear groupnilpotent matrixminimal set of generatorsC-indexlinear transformations of a vector spacenonsingular matrices over a finite fieldsemigroup of linear transformations

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Semigroups of transformations, relations, partitions, etc. (20M20) Generators, relations, and presentations of groups (20F05) Free semigroups, generators and relations, word problems (20M05) Linear transformations, semilinear transformations (15A04)

Related Items (8)

ON AUTOMORPHISM GROUPS OF ENDOMORPHISM SEMIGROUPS OF FINITE ELEMENTARY ABELIAN GROUPS ⋮ Bijective Cremona transformations of the plane ⋮ Semigroups of rectangular matrices under a sandwich operation ⋮ Free properly discontinuous actions on homotopy surfaces ⋮ Ranks and isomorphism theorems of semigroups of linear transformations with restricted range ⋮ On some properties of vector space based graphs ⋮ THE REGULAR PART OF A SEMIGROUP OF LINEAR TRANSFORMATIONS WITH RESTRICTED RANGE ⋮ Intersection graphs of general linear groups

Cites Work

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• Some applications of the first cohomology group
• Generators for Simple Groups
• The countability index of the endomorphism semigroup of a vector space
• On generating the simple group 𝐿𝐹(2,2^{𝑁}) by two operators of periods two and three

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