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.

KEYWORDS:

• Character tables
• closed subsets
• dual C-algebras
• finite groups
• generalized wreath products
• table algebras

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 20C99
• 20E22

Acknowledgments

The authors would like to thank the anonymous referee and H. Blau for useful suggestions, which have improved the quality of the paper. The main work of this paper was done during the visit of the first author at Eastern Kentucky University in 2015. He appreciates the hospitality of the second author and EKU.