An Enumeration of the Supercharacter Theories of $C_p\times C_2\times C_2$ for Prime $p$

Abstract

The supercharacter theories of $C_p\times C_2\times C_2$ were classified in the language of Schur rings by Evdokimov, Kovács, and Ponomarenko in [EKP16]. It was shown that every nontrivial supercharacter theory of $C_p\times C_2\times C_2$ 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 $C_p\times C_2\times C_2$ 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.

29 pages

References in corpus (1)

• Supercharacter theories and Schur rings