On groups of hyperbolic length
type: Item
instance of: scholarly article
title: On groups of hyperbolic length
zbMATH Open document ID: 0881.20020
DOI: 10.1007/BF02937329
author: Douglas P. Brozovic
author: Ronald Solomon
published in: Israel Journal of Mathematics
publication date: 1998-01-05T00:00:00Z
review text: This paper concerns the function \(\ell(G)\), the length of the longest chain of subgroups of \(G\), for \(G\) a finite Lie type group. Such a group \(G\) is said to be of hyperbolic length if no chain of maximal length for \(G\) can include a parabolic subgroup. Using detailed information on the maximal subgroups of \(G\), the authors prove that to calculate \(\ell(G)\), one need consider only some very special types of maximal subgroups. In particular, they obtain that the maximal parabolic subgroups are almost always enough. Their results imply that, for each prime \(p\), there exist only finitely many (possibly \(0\)) finite Lie type groups \(G\) in characteristic \(p\) with \(G\) of hyperbolic length. This strengthens a result of \textit{R. Solomon} and \textit{A. Turull} [J. Lond. Math. Soc., II. Ser. 44, No. 3, 437-444 (1991; Zbl 0776.20007)]. (Also submitted to MR).
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 20D30
Mathematics Subject Classification ID: 20E28
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 1033780
zbMATH Keywords: lengths of maximal chains
zbMATH Keywords: lengths of chains of subgroups
zbMATH Keywords: Lie type groups
zbMATH Keywords: maximal subgroups
zbMATH Keywords: parabolic subgroups
zbMATH Keywords: groups of parabolic lengths
reviewed by: Alexandre Turull
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1033780