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

Alexander Lang

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arXiv · 1609.07182

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

Alexander Lang

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Abstract

The supercharacter theories of $C_p \times C_2 \times C_2$ were classified in the language of Schur rings by Evdokimov, Kov\'acs, 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.

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BibTeX RIS

Alexander Lang. 2016-09-22. An Enumeration of the Supercharacter Theories of $C_p \times C_2 \times C_2$ for Prime $p$. https://arxiv.org/abs/1609.07182

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