Linear p- Brauer characters and p-blocks

摘要

Let G be a finite group and p a prime divisor of | G |. Denote by IBr(G) and LBr(G) the sets of irreducible p-Brauer characters and linear p-Brauer characters of G, respectively. It is known that IBr(G) = LBr(G) if and only if P ? E Sylp(G) is normal and G/P is abelian. We consider the local situation in this note. Let B be a p-block of G. We characterize the finite groups G with IBr(B) ? LBr(G). And we get some results related to those of Holm, Willems and Isaacs, Smith.