Nilpotency property in table algebras (Q1977548)

The concept of a table algebra was defined by \textit{Z. Arad} and \textit{H. I. Blau} [J. Algebra 138, No. 1, 137-185 (1991; Zbl 0790.20015)]. This is a finite-dimensional algebra over the complex field \(\mathbb{C}\) with certain properties. The concepts of composition series and composition factors and consequently nilpotency for table algebras are defined by \textit{H. I. Blau} [J. Algebra 177, No. 1, 297-337 (1995; Zbl 0895.20006)]. In the paper under review the author proves that the dual of a nilpotent table algebra is also a nilpotent table algebra.