On Isomorphisms of a Brauer Character Ring onto Another, II

This article is a continuation of my article, “On Isomorphisms of a Brauer Character Ring onto Another” (K. Yamauchi, 1996, Tsukuba J. Math.20, 207–212). In this article we state a necessary and sufficient condition under which an isomorphism λ of a Brauer character ring onto another preserves an inner product. We also state the relations between λ and blocks of group algebras of finite groups.