An S-ring (Schur ring) is said to be central if it is contained in the center of a group ring. We introduce the notion of a generalized Schur group, i.e., a finite group such that all central S-rings over this group are Schurian. It generalizes the notion of a Schur group in a natural way, and for Abelian groups, the two notions are equivalent. We prove basic properties and present infinite families of non-Abelian generalized Schur groups.
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I am grateful to the referee whose comments helped me to considerably improve the presentation of material in the paper.
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Translated from Algebra i Logika, Vol. 62, No. 2, pp. 247-265,March-April, 2023. Russian DOI: https://doi.org/10.33048/alglog.2023.62.205.
G. K. Ryabov is supported by Russian Science Foundation, project No. 22-71-00021.
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Ryabov, G.K. Generalized Schur Groups. Algebra Logic 62, 166–178 (2023). https://doi.org/10.1007/s10469-024-09734-5
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DOI: https://doi.org/10.1007/s10469-024-09734-5