ON RELATIVE HEIGHT ZERO BRAUER CHARACTERS

A. Laradji
Let N G where G is a finite group and let B be a p-block of G, where p is a prime. A Brauer character ¾ IBr p (B) is said to be of relative height zero with respect to N provided that the height of is equal to that of an irreducible constituent of N . Now assume G is p-solvable. In this paper, we count the number of relative height zero irreducible Brauer characters of B with respect to N that lie over any given ³ ¾ IBr p (N ). As a consequence, we show that if D is a defect group of B and Ç B
more » ... s the unique p-block of N N G (D) with defect group D such that Ç B G B, then B and Ç B have equal numbers of relative height zero irreducible Brauer characters with respect to N .
doi:10.18910/26016 fatcat:qvfekssx5vfdrptg3vtyy67xzy