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On twisted group ring isomorphism problem for p-groups

Part of: Representation theory of groups Rings and algebras arising under various constructions Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  16 February 2024

Gurleen Kaur ,
Surinder Kaur Open the ORCID record for Surinder Kaur [Opens in a new window]  and
Pooja Singla
Gurleen Kaur
Affiliation:
Indian Institute of Science Education and Research Mohali, Knowledge City, Mohali, 140 306, India
Surinder Kaur
Affiliation:
Department of Mathematics, School of Engineering and Sciences, SRM University AP, Amaravati, Andhra Pradesh, 522502, India
Pooja Singla*
Affiliation:
Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, 208016, India
*
Corresponding author: Pooja Singla; Email: [email protected]
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Abstract

In this article, we explore the problem of determining isomorphisms between the twisted complex group algebras of finite $p$-groups. This problem bears similarity to the classical group algebra isomorphism problem and has been recently examined by Margolis-Schnabel. Our focus lies on a specific invariant, referred to as the generalized corank, which relates to the twisted complex group algebra isomorphism problem. We provide a solution for non-abelian $p$-groups with generalized corank at most three.

Keywords

twisted group algebrasprojective representationsSchur multiplier

MSC classification

Primary: 16S35: Twisted and skew group rings, crossed products
Secondary: 20C25: Projective representations and multipliers 20E99: None of the above, but in this section
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 66 , Issue 2 , May 2024 , pp. 368 - 381
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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