Dolfi定理的Brauer形式

Brauer Versions of Dolfi Theorem

给定一个p-可解群G以及G的一个关于该素数p的不可约B rauer特征标χ.证明了χ在G的任意一个子群N上的限制的不可约分量的次数可被N及其在G中的正规化子满足的条件所控制,从而把D o lfi定理从复特征标推广到B rauer特征标情形,并得到了p-可解群中关于B rauer特征标的C lifford定理的某种推广.

Given a p-solvable group G and an irreducible Brauer character X of G with respect to the prime p. It is proved in this paper that the degrees of irreducible constituents of the restriction of X to an arbitrary subgroup N in G can be controlled by some conditions on N and on the normalizer of N in G. This finding has not only promoted Dolfi theorem from complex characters to Brauer characters, it has also generalized Clifford theorem on Brauer characters in p-solvable groups.