Automorphisms and nonabelian cohomology: An algorithm
type: Item
instance of: scholarly article
title: Automorphisms and nonabelian cohomology: An algorithm
zbMATH Open document ID: 0798.20002
DOI: 10.1016/0024-3795(93)90249-N
author: Klaus W. Roggenkamp
author: Leonard L. Scott
published in: Linear Algebra and its Applications
publication date: 1994-11-09T00:00:00Z
review text: Let \(Z_ p\) be the field of \(p\) elements. Let \(G\), \(H\) be finite \(p\)- groups. The objective of this paper is to construct an algorithm to test whether the group rings \(Z_ pG\), \(Z_ pH\) are isomorphic or not when considered as augmented algebras. The methods of the algorithm are explained at length in the paper. The paper is not easily amenable to summary but it may suffice to state that the authors ingeniously develop techniques available in the cohomology of groups to construct extension homomorphisms of given homomorphisms, these being mainly unique up to conjugacy. The method has already, in modified form, been implemented on a computer.
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20J06
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20C40
zbMATH DE Number: 484450
zbMATH Keywords: isomorphism problem
zbMATH Keywords: isomorphic as augmented algebras
zbMATH Keywords: finite \(p\)-groups
zbMATH Keywords: group rings
zbMATH Keywords: cohomology of groups
zbMATH Keywords: extension homomorphisms
MaRDI profile type: Publication
cites work: Decomposition of the Relation Modules of a Finite Group
cites work: Q3253828
cites work: The structure over \(\mathbb{Z}[q,q^{-1}]\) of Hecke orders of dihedral groups
cites work: Isomorphisms of modular group algebras: An algorithm and its application to groups of order \(2^ 6\)
description: scientific article; zbMATH DE number 484450