Conjugacy classes in unitriangular matrices.
type: Item
instance of: scholarly article
title: Conjugacy classes in unitriangular matrices.
zbMATH Open document ID: 1045.20045
DOI: 10.1016/S0024-3795(03)00371-9
author: A. Vera-López
author: J. M. Arregi
published in: Linear Algebra and its Applications
publication date: 2003-08-25T00:00:00Z
review text: Let \(G_n=G_n(q)\) be the group of the upper unitriangular matrices of size \(n\times n\) over \(\text{GF}(q)\), the finite field with \(q=p^t\) elements. Higman has conjectured that, for each \(n\), the number of conjugacy classes of elements of \(G_n\) is a polynomial expression in \(q\). In the paper under review, the authors develop the algorithm given by them [in J. Algebra 177, No. 3, 899-925 (1995; Zbl 0839.20061)] and introduce new ideas and theoretical properties which lead to get the conjugacy vector of \(G_n\) for \(n\leq 13\). In particular, they conclude that, for these values, the number of conjugacy classes of \(G_n\) is a polynomial in \(q\) with integral coefficients and degree \([n(n+6)/12]\). Thus, Higman's conjecture holds for \(n\leq 13\).
reviewed by: A. Iranmanesh
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 20E45
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20-04
zbMATH DE Number: 1970612
zbMATH Keywords: unitriangular matrices
zbMATH Keywords: Higman's conjecture
zbMATH Keywords: numbers of conjugacy classes
zbMATH Keywords: finite \(p\)-groups
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1970612