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Structures of commutative table algebras determined by their character tables and applications to finite groups

ABSTRACT Structures of table algebras determined by their character tables are studied in [6]. In this paper we continue the research in this direction. In particular, we investigate the conditions under which the character table with a zero submatrix yields a generalized wreath product for a commutative table algebra. Applications to finite groups are also discussed, and some new and known results are obtained as direct consequences.