On thin residues and basis digraphs of nilpotent table algebras and applications to nilpotent groups

In this paper we study characterizations of nilpotent table algebras in terms of thin residues; thin residue matrices; thin residue digraphs; and basis digraphs. We will also discuss applications to nilpotent groups. In particular, we give a conceptual explanation of the results in Takegahara and Yoshida (2008) [TY].