Indecomposable endo-permutation modules over p-groups
type: Item
instance of: scholarly article
title: Indecomposable endo-permutation modules over p-groups
zbMATH Open document ID: 0603.20009
DOI: 10.1016/0021-8693(86)90233-4
author: Everett C. Dade
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: Let \({\mathfrak O}\) be a valuation ring with residue field \({\mathfrak F}\) of characteristic \(p>0\) and P a p-group. For an \({\mathfrak O}P\)-lattice \({\mathfrak K}\), let \({\mathfrak E(K)}=End_{{\mathfrak O}P}({\mathfrak K})/J(End_{{\mathfrak O}P}(K))\). In the literature, there are two notions of ''absolutely indecomposable'' lattice. One, due to \textit{J. A. Green} [Math. Z. 70, 430- 445 (1959; Zbl 0086.024)] is that \({\mathfrak E(K)}\) should be a purely inseparable extension of \({\mathfrak F}\). The other, due to \textit{B. Huppert} [Arch. Math. 26, 242-249 (1975; Zbl 0304.20008)] is that \({\mathfrak E(K)}\) should be isomorphic to \({\mathfrak F}.\) In an earlier paper [Ann. Math., II. Ser. 107, 459-494 (1978; Zbl 0395.16007)], the author proved that any indecomposable endo-permutation \({\mathfrak O}P\)-lattice is absolutely indecomposable. Unfortunately, he only proved absolute indecomposability in the sense of Green, whereas he wanted it in the sense of Huppert. Here, he uses Green's methods to obtain the result he actually wanted in the earlier paper.
Mathematics Subject Classification ID: 20C10
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16H05
zbMATH DE Number: 3973133
zbMATH Keywords: endo-permutation module
zbMATH Keywords: p-group
zbMATH Keywords: indecomposable endo-permutation \({\mathfrak O}P\)-lattice
zbMATH Keywords: absolute indecomposability
reviewed by: William H. Gustafson
MaRDI profile type: Publication
full work available at URL: 0021-8693(86)90233-4
OpenAlex ID: W1998547117
cites work: Endo-permutation modules over p-groups. I
cites work: Q5572378
cites work: On the indecomposable representations of a finite group
cites work: Blocks of modular representations
cites work: A transfer theorem for modular representations
cites work: Relative module categories for finite groups
cites work: Bemerkungen zur modularen Darstellungstheorie. I: Absolut unzerlegbare Moduln
description: scientific article; zbMATH DE number 3973133