Isomorphisms of modular group algebras: An algorithm and its application to groups of order \(2^ 6\)
type: Item
instance of: scholarly article
title: Isomorphisms of modular group algebras: An algorithm and its application to groups of order \(2^ 6\)
zbMATH Open document ID: 0782.20001
author: Martin Wursthorn
published in: Journal of Symbolic Computation
publication date: 1993-08-25T00:00:00Z
review text: For finite \(p\)-groups \(G\) and \(H\) denote by \(F(G)\) and \(F(H)\) their group rings over the field \(F = Z/pZ\). It is known that \(F(G)\cong F(H)\) implies \(G \cong H\) when \(|G|\leq p^ 5\) but in general the isomorphism problem is unresolved. The author resolves the situation for \(|G|= 2^ 6\) (and shows that the ring isomorphism does imply the group isomorphism) by developing an algorithm for the lifting of homomorphisms based on an idea of \textit{K. W. Roggenkamp} and \textit{L. L. Scott} [to appear] and implementing it for groups of order \(2^ 6\). The author notes that the implementation uses the system SISYPHOS which does symbolic computations in modular group rings of \(p\)-groups. CAYLEY was used to calculate the group invariants.
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20C40
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20C20
zbMATH DE Number: 370652
zbMATH Keywords: finite \(p\)-groups
zbMATH Keywords: group rings
zbMATH Keywords: isomorphism problem
zbMATH Keywords: algorithm
zbMATH Keywords: lifting of homomorphisms
zbMATH Keywords: groups of order \(2^ 6\)
zbMATH Keywords: symbolic computations
zbMATH Keywords: modular group rings
reviewed by: W. E. Deskins
MaRDI profile type: Publication
full work available at URL: jsco.1993.1015
OpenAlex ID: W2060551669
DOI: 10.1006/JSCO.1993.1015
description: scientific article; zbMATH DE number 370652