On Schur Rings over Infinite Groups

  • Nicholas Bastian
  • Jaden Brewer
  • Stephen Humphries
  • Andrew MisseldineEmail author
  • Cache Thompson


Schur rings are a type of subring of the group ring that is determined by a partition of the group. Past literature has exclusively focused on the finite group case. This paper extends many classic results about Schur rings to infinite groups, including Leung-Man’s classification of Schur rings over finite cyclic groups which is extended to the infinite cyclic group, as well as all torsion-free locally cyclic groups. Schurs rings over free groups and free products are also considered.


Schur ring Cyclic group Locally cyclic group Torsion-free abelian group Laurent polynomial ring Association scheme Free group Free product 

Mathematics Subject Classification (2010)

20C07 16S34 20E25 20C05 05E30 


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Southern Utah UniversityCedar CityUSA
  2. 2.Brigham Young UniversityProvoUSA

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