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  2. Toward a classification of the supercharacter theories of Cp × Cp
Author(s)
Abstract

In this paper, we study the supercharacter theories of elementary abelian p-groups of order p2. We show that the supercharacter theories that arise from the direct product construction and the ∗-product construction can be obtained from automorphisms. We also prove that any supercharacter theory of an elementary abelian p-group of order p2 that has a non-identity superclass of size 1 or a non-principal linear supercharacter must come from either a ∗-product or a direct product. Although we are unable to prove results for general primes, we do compute all of the supercharacter theories when p = 2, 3, 5, and based on these computations along with particular computations for larger primes, we make several conjectures for a general prime p.
Format
Article
Identifier(s)
10.1017/S0013091522000438
Publication Date
2022-10-12
Publication Title
Proceedings of the Edinburgh Mathematical Society
Publisher
Cambridge University Press
First Page
1
Last Page
21
Keywords
Subject
Rights
http://rightsstatements.org/vocab/InC/1.0/
License
Creative Commons Attribution 4.0
Community
Department of Mathematical Sciences
Permalink https://oaks.kent.edu/article/toward-classification-supercharacter-theories-cp-cp
Burkett, S., & Lewis, M. (2022). Toward a classification of the supercharacter theories of Cp × Cp (1–). Proceedings of the Edinburgh Mathematical Society. https://doi.org/10.1017/S0013091522000438
Burkett, Shawn, and Mark Lewis. 2022. “Toward a Classification of the Supercharacter Theories of Cp × Cp”. Proceedings of the Edinburgh Mathematical Society. https://doi.org/10.1017/S0013091522000438.
Burkett, Shawn, and Mark Lewis. Toward a Classification of the Supercharacter Theories of Cp × Cp. Proceedings of the Edinburgh Mathematical Society, 12 Oct. 2022, https://doi.org/10.1017/S0013091522000438.