Source: Proc. Japan Acad. Ser. A Math. Sci.
Volume 88, Number 3
We give a reduction theorem for Brauer’s height zero conjecture.
T. R. Berger and R. Knörr, On Brauer's height 0 conjecture, Nagoya Math. J. 109 (1988), 109–116.
Mathematical Reviews (MathSciNet): MR931954
E. C. Dade, Counting characters in blocks, II, J. Reine Angew. Math. 448 (1994), 97–190.
D. Gluck and T. R. Wolf, Brauer's height conjecture for $p$-solvable groups, Trans. Amer. Math. Soc. 282 (1984), no. 1, 137–152.
Mathematical Reviews (MathSciNet): MR728707
B. Külshammer and L. Puig, Extensions of nilpotent blocks, Invent. Math. 102 (1990), no. 1, 17–71.
M. Murai, Block induction, normal subgroups and characters of height zero, Osaka J. Math. 31 (1994), no. 1, 9–25.
M. Murai, A remark on Brauer's height zero conjecture, J. Math. Kyoto Univ. 35 (1995), no. 4, 607–610.
M. Murai, Normal subgroups and heights of characters, J. Math. Kyoto Univ. 36 (1996), no. 1, 31–43.
H. Nagao and Y. Tsushima, Representations of finite groups, Academic Press, New York, 1989.
Mathematical Reviews (MathSciNet): MR998775
G. Navarro and P. H. Tiep, Brauer's height zero conjecture for the 2-blocks of maximal defect. (to appear in J. Reine Angew. Math.).
G. R. Robinson, Cancellation theorems related to conjectures of Alperin and Dade, J. Algebra 249 (2002), no. 1, 196–219.