Projective supercharacter theory

Abstract

The idea of supercharacters for ordinary characters of a finite group G was introduced by Diaconis and Isaacs and further extended to Brauer characters by Chen and Lewis. The twin concepts of supercharacters and superclasses are further extended here to α-characters of G for α a complex-valued 2-cocycle of G. An α-quasi-supercharacter theory of G arises when the set of α-quasi-supercharacters of G are compatible with the set of α-regular quasi-superclasses of G. The structure of solvable groups that have exactly two α-quasi-supercharacter theories is determined.

Communicated by Mark L. Lewis

Keywords:

• Projective characters
• supercharacters
• superclasses

2010 Mathematics Subject Classification:

• Primary: 20C25

Acknowledgments

The authors would like to thank the referee for improving the readability of this paper as well as suggesting two further topics for future research.