广义Gagola特征标的注记

A Note on Generalized Gagola Characters

设χ∈Irr(G)是广义Gagola特征标,V(χ)={χ(g)|g∈G}.证明了χ是广义Gagola特征标,当且仅当χ忠实,并且V(χ)恰好有3个Galois-轨道.在此基础上,得到经典Gagola特征标的一个充要条件.

Let G be a finite group, X ∈ Irr（G） be a generalized Gagola character, and V（X） = { X （g） ｜ g ∈ G }. This note gives a neces- sary and sufficient condition for the generalized Gagola character,and it is also proved that X is a generalized Gagola Character if and only if X is faithful and ｜V（Z）｜ =3.