On a conjecture of P. Landrock
type: Item
instance of: scholarly article
title: On a conjecture of P. Landrock
zbMATH Open document ID: 0628.20008
DOI: 10.1016/0021-8693(86)90247-4
author: Tetsuro Okuyama
author: Y. Tsushima
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: Let G be a finite group, k an algebraically closed field of prime characteristic p, and J the radical of kG. Landrock conjectured that \(J^ i/J^{i+1}\) is self dual as a (right) kG-module for all i. The authors show that this is false for the Mathieu group \(G=M_{11}\) of degree 11 and \(p=11\). They give another counterexample where G is a solvble group. However they show that Landrock's conjecture is true for \(G=A_ n\), \(GL_ n(g)\), \(SL_ n(q)\), and other groups.
reviewed by: B.G.Basmaji
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16Nxx
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 4021420
zbMATH Keywords: self dual kG-module
zbMATH Keywords: finite group
zbMATH Keywords: radical
zbMATH Keywords: Mathieu group
zbMATH Keywords: counterexample
zbMATH Keywords: solvble group
Wikidata QID: Q122981360
MaRDI profile type: Publication
full work available at URL: 0021-8693(86)90247-4
OpenAlex ID: W2022989346
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cites work: Q3035669
cites work: Blocks with a cyclic defect group
cites work: Group extensions and splitting modules
cites work: On the conjugacy classes in the unitary, symplectic and orthogonal groups
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description: scientific article; zbMATH DE number 4021420