An Enumeration of the Supercharacter Theories of C_p × C₂ × C₂ for Prime p

2016/09/22 by Lang, Alexander
#FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1609.07182

Abstract

The supercharacter theories of C_p × C₂ × C₂ were classified in the language of Schur rings by Evdokimov, Kovács, and Ponomarenko in [EKP16]. It was shown that every nontrivial supercharacter theory of C_p × C₂ × C₂ can be constructed as a wedge product, a direct product, or is generated by automorphisms. We use this classification to give a precise count of the distinct supercharacter theories of C_p× C₂× C₂ and describe when a supercharacter theory can be constructed by more than one method. We also present an alternative proof of the classification using the language of supercharacter theories.

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