Vertices, blocks, and virtual characters (Q919459)

This paper is closely associated with the works of \textit{M. Broué} and \textit{L. Puig} [J. Algebra 63, 306-317 (1980; Zbl 0428.20005)] and \textit{L. Puig} [Math. Z. 176, 265-292 (1981; Zbl 0464.20007)]. Its first result deals with G-algebras and pointed groups and has an important consequence (Corollary 2.7) relating vertices and blocks. In particular this corollary allows a special case of Brauer's Second Main Theorem to be strengthened. The second result of this paper gives us an extension of Broué-Puig's construction for virtual characters of a finite group from their work above. There is also a discussion of some generalization of the first result.