Finite Subgroups of Group Rings: A survey

2018/09/03 by Leo Margolis, Ángel del Rı́o, Margolis, Leo +1 · 1 citation
Mathematics · #16S34 #16U60 #20C05 #20C10 #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1809.00718

openalex publication_date 2018/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the 1940's Graham Higman initiated the study of finite subgroups of the unit group of an integral group ring. Since then many fascinating aspects of this structure have been discovered. Major questions such as the Isomorphism Problem and the Zassenhaus Conjectures have been settled, leading to many new challenging problems. In this survey we review classical and recent results, sketch methods and list questions relevant for the state of the art.

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• The N-prime graph and the Subgroup Isomorphism Problem

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