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

Structures of table algebras determined by their character tables are studied in [6 Blau, H., Xu, B. (2014). Irreducible characters of wreath products in reality-based algebras and applications to association schemes. J. Algebra 412 (2014), 155–172.[Crossref] , [Google Scholar]]. 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.