特征标对映与内幂零群

Character correspondeces and inner nilpotent groups

假定有限群A互素地作用在有限群G上.设B≤A.对于Glauberman Isaacs特征标对映π和χ∈IrrA(G),有猜想:χπ(G,A)是χπ(G,B)CG(A)的一个不可约成份.证明了这一猜想对于内幂零群是成立的.

Assume that finite group A acts coprimely on finite group B and B≤A.For Glauberman-Isaacs character correspondences π and the character χ∈I_(rrA)(G),it was conjectured that χπ(G,A) is an irreducible constituent of χπ(G,B)_(C_G(A)).In this note,it is proved that the conjecture is true for the inner nipotent groups.