On Schur rings over infinite groups III

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On Schur rings over infinite groups III

Bastian, Nicholas; Misseldine, Andrew

Journal of algebraic combinatorics, 12/2023, Volume: 58, Issue: 4

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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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