Linear p- Brauer characters and p-blocks. (3rd April 2017) - Chen, Xiaoyou; Zeng, Jiwen
Abstract: 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 ∈ Syl p ( 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.