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The structure of Schur rings over cyclic groups of square-free order. (English) Zbl 0916.05079

Schur rings are a class of group algebras over finite groups, introduced by I. Schur in 1933. The theory of Schur rings was developed in the well-known book by H. Wielandt [Finite permutation groups (1964; Zbl 0138.02501)].
In this paper the author gives a characterization of Schur rings over cyclic groups of square-free order in terms of topology, that is, he shows that each Schur ring over a cyclic group of square-free order \(n\) is uniquely determined by a finite topology on the set of prime divisors of \(n\) and by a family of finite groups satisfying certain additional conditions.

MSC:

05E99 Algebraic combinatorics
20C05 Group rings of finite groups and their modules (group-theoretic aspects)
54H99 Connections of general topology with other structures, applications

Citations:

Zbl 0138.02501
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