A note on the support of block idempotents
Let \(G\) be a finite group and \(K\) be a field of characteristic \(p\). For a block idempotent \(f\) of \(KG\) let \(O_f(G)\) denote the subgroup of \(G\) generated by the support of \(f\). It has been proved by \textit{G. Tiedt} [Beitr. Algebra Geom. 32, 47-51 (1991; Zbl 0784.20004)] that if \(G\) is a \(p\)-solvable group and \(f\) belongs to a block of maximal defect, then \(O_f (G) \leq O_{p'}(G)\). In earlier works, the author proved that for a principal block idempotent \(f\) the group \(O_f(G)\) is contained in the generalized \(p'\)-core \(O_{p^*} (G)\). In this paper the author generalizes his results and proves \(O_f (G) \leq O_{p^*} (G)\) whenever a defect group of \(f\) contains a Sylow \(p\)-subgroup of \(O_{p^*p} (G)\).
scientific article; zbMATH DE number 743526