Minimal logarithmic signatures for finite groups of Lie type
type: Item
instance of: scholarly article
title: Minimal logarithmic signatures for finite groups of Lie type
zbMATH Open document ID: 1202.94199
author: Nidhi Singhi
author: Nikhil Singhi
author: Spyros S. Magliveras
published in: Designs, Codes and Cryptography
publication date: 2010-05-19T00:00:00Z
review text: The paper proposes to use minimal logarithmic signatures for finite groups of Lie type. The method presented in the paper is working for the families \(\text{PSL}_n(q)\) and \(\text{PSp}_{2n}(q)\) and uses Singer subgroups and the Levi decomposition of parabolic subgroups for these groups. To study the minimal logarithmic signature (MLS) conjecture, the authors give some basic results about LS for an arbitrary subset \(A\) of a group \(G\). Their aim is to obtain general methods to construct MLS for (simple) groups. By using Remark 3.12, they describe parabolic subgroups, sharply transitive sets and standard Levi subgroups for the corresponding (simple) groups. Then, they use the remark as a tool to create MLSs and other interesting LSs for such groups. They also obtain MLSs for \(\text{GL}_n(q)\) and \(\text{PGL}_n(q)\) using a slightly different method than \textit{W. Lempken} and \textit{Tran van Trung} [Exp. Math. 14, No. 3, 257--269 (2005; Zbl 1081.94038)]. The authors construct MLSs for the groups \(\text{GL}_{n}(q)\), \(\text{PGL}_n(q)\), \(\text{SL}_n(q)\) and \(\text{Sp}_{2n}(q)\). The blocks of the LSs are obtained from Singer subgroups of the classical (sub)groups. This also produces a spread in the corresponding projective or polar space. Their methods are general and may prove sufficiently strong as tools for constructing MLSs for all finite simple groups.
reviewed by: Ferruh Özbudak
Mathematics Subject Classification ID: 94A60
Mathematics Subject Classification ID: 11T71
Mathematics Subject Classification ID: 14G50
Mathematics Subject Classification ID: 20D06
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 94A62
zbMATH DE Number: 5709170
zbMATH Keywords: logarithmic signatures
zbMATH Keywords: finite groups of Lie type
zbMATH Keywords: simple groups
zbMATH Keywords: Singer groups
Wikidata QID: Q115384024
MaRDI profile type: Publication
full work available at URL: s10623-010-9369-9
OpenAlex ID: W2065716701
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DOI: 10.1007/S10623-010-9369-9
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description: scientific article; zbMATH DE number 5709170