Brauer characters preserve heights in p-solvable groups

Abstract

Let p be a prime number and let N be a normal subgroup of a finite p-solvable group G. Assume that b is a p-block of N with defect group D and B is a p-block of G covering b. Let $b^{⁎}$ be the Brauer first main correspondent of b in $N_N\left(D\right)$, and $B^{⁎}$ be the Harris–Knörr correspondent of B in $N_G\left(D\right)$. Suppose that every irreducible Brauer character in $\mathrm{IBr}\left(b\right)$ is of height zero. Then there is a height preserving bijection from $\mathrm{IBr}\left(B\right)$ onto $\mathrm{IBr}\left(B^{⁎}\right)$. This is a Brauer character version of a result obtained by G. Navarro and B. Späth (2014) [23].