The twisted group ring isomorphism problem over fields

Similarly to how the classical group ring isomorphism problem asks, for a commutative ring R , which information about a finite group G is encoded in the group ring RG , the twisted group ring isomorphism problem asks which information about G is encoded in all the twisted group rings of G over R ....

Full description

Saved in:
Bibliographic Details
Published in:Israel journal of mathematics 2020-07, Vol.238 (1), p.209-242
Main Authors: Margolis, Leo, Schnabel, Ofir
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Commutativity
Fields (mathematics)
Group theory
Group Theory and Generalizations
Isomorphism
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Rings (mathematics)
Theoretical
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Similarly to how the classical group ring isomorphism problem asks, for a commutative ring R , which information about a finite group G is encoded in the group ring RG , the twisted group ring isomorphism problem asks which information about G is encoded in all the twisted group rings of G over R . We investigate this problem over fields. We start with abelian groups and show how the results depend on the characteristic of R . In order to deal with non-abelian groups we construct a generalization of a Schur cover which exists also when R is not an algebraically closed field, but still linearizes all projective representations of a group. We then show that groups from the celebrated example of Everett Dade which have isomorphic group algebras over any field can be distinguished by their twisted group algebras over finite fields.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-020-2017-9