Projective supercharacter theory. Issue 8 (2nd August 2020)

• Record Type: Journal Article
• Authors: Finnegan, C.; Higgs, R. J.
• Is Part Of: Communications in algebra. Volume 48:Issue 8(2020)
• Page Start: 3447
• Page End: 3458
• Publication Date: 2020-08-02
• Subjects: Projective characters -- supercharacters -- superclasses; Primary: 20C25; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2020.1739696
• Languages: English
• ISSNs: 0092-7872

Abstract

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