A characterization of permutation modules extending a theorem of Weiss
type: Item
instance of: scholarly article
title: A characterization of permutation modules extending a theorem of Weiss
author: John MacQuarrie
author: Pavel Zalesskij
published in: Documenta Mathematica
publication date: 2020-10-08T00:00:00Z
review text: Summary: Let \(G\) be a finite \(p\)-group with normal subgroup \(N\). A celebrated theorem of A. Weiss gives a sufficient condition for a \(\mathbb{Z}_pG\)-lattice to be a permutation module, looking only at its restriction to \(N\) and its \(N\)-fixed points. In case \(N\) has order \(p\), we extend the condition of Weiss to a characterization.
Mathematics Subject Classification ID: 20C11
zbMATH DE Number: 7258093
zbMATH Keywords: permutation modules
zbMATH Keywords: finite \(p\)-groups
MaRDI profile type: Publication
cites work: Q3999421
cites work: Tensor induction of relative syzygies
cites work: On Scott Modules and p-Permutation Modules: An Approach through the Brauer Morphism
cites work: Representations of cyclic groups in rings of integers. I
cites work: Virtually free groups and integral representations
cites work: Infinitely generated pseudocompact modules for finite groups and Weiss' theorem
cites work: Q4858090
cites work: Lattices and cohomological Mackey functors for finite cyclic \(p\)-groups
cites work: Rigidity of \(p\)-adic \(p\)-torsion
cites work: Infinitely generated virtually free pro‐p groups and p‐adic representations
DOI: 10.25537/DM.2020V25.1159-1169
description: scientific article; zbMATH DE number 7258093