Project supported by the NNSF of China(No.10571128);the SRFDP of China(No.20060285002);Young Teachers Fund of College of Mathematics and Physics,Chongqing University(2005)
the National Natural Science Foundation of China (No. 10571128); the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20060285002).Acknowledgment The first author is grateful to Professor Ren Yongcai for his helps. Both authors thank the referee for making numerous suggestions and pointing out misprints.
The aim of this note is to classify the finite meta-abelian groups in which every irreducible character vanishes on at most three conjugacy classes.