The exact number of conjugacy classes of the Sylow \(p\)-subgroups of \(\text{GL}(n,q)\) modulo \((q-1)^{13}\).

DOI10.1016/J.LAA.2008.03.017zbMath1141.20008OpenAlexW1991019064MaRDI QIDQ929487

Leyre Ormaetxea, Francisco José Vera López, Jesus Maria Arregi, Antonio Vera-López

Publication date: 17 June 2008

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

Full work available at URL: https://doi.org/10.1016/j.laa.2008.03.017

zbMATH Keywords

numbers of conjugacy classesfinite \(p\)-groupsgroups of upper unitriangular matricesHigman conjectureprimitive canonical matrices

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Arithmetic and combinatorial problems involving abstract finite groups (20D60)

Related Items (5)

Equalities on the number of conjugacy classes of the Sylow \(p\)-subgroups of \(GL(n,q)\). ⋮ A generalization of Catalan numbers ⋮ Groups, Graphs, and Hypergraphs: Average Sizes of Kernels of Generic Matrices with Support Constraints ⋮ Counting conjugacy classes for unitriangular matrices. ⋮ Combinatorics related to Higman's conjecture. I: Parallelogramic digraphs and dispositions

Cites Work

• Unnamed Item
• Conjugacy classes in Sylow \(p\)-subgroups of \(GL(n,q)\)
• Conjugacy classes in unitriangular matrices.
• Some algorithms for the calculation of conjugacy classes in the Sylow \(p\)-subgroups of \(\text{GL}(n,q)\)
• Enumerating p -Groups. I: Inequalities
• Conjugacy classes in Sylow p-subgroups of GL(n,q), II
• Conjugacy classes in sylow p-subgroups of GL(n, q), IV
• On the number of conjugacy classes of the sylow p-subgroups of GL(n,q)

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