Generalized Schur groups

G. K. Ryabov

Algebra i logika, Tome 62 (2023) no. 2, pp. 247-265.

Résumé

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.

Détail

Keywords: Schur rings, Schur groups, $p$-groups, Camina groups, dihedral groups.

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