On Schur Rings over Infinite Groups III

2019/06/22 by Nicholas Bastian, Bastian, Nicholas, Andrew Misseldine +1
Engineering · Mathematics · Medicine · #05b10 #05e30 #16s34 #20c07 #20e22 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Synthesis of Organic Compounds #graph theory and CDMA systems

paper · doi:10.48550/arxiv.1906.09469

openalex publication_date 2019/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the paper, we develop further the properties of Schur rings over infinite groups, with particular emphasis on the virtually cyclic group \Z×\Z_p, where p is a prime. We provide structure theorems for primitive sets in these Schur rings. In the case of Fermat and safe primes, a complete classification theorem is proven, which states that all Schur rings over \Z×\Z_p are traditional. We also draw analogs between Schur rings over \Z×\Z_p and partitions of difference sets over \Z_p.

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