2020/07/24 by Burkett, Shawn T., Lewis, Mark L.
#FOS: Mathematics #Group Theory (math.GR) #Primary: 20C15 #Secondary 20D15
paper · doi:10.48550/arxiv.2007.12503
In this paper, we study the superscharacter 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 nonidentity superclass of size 1 or a nonprincipal 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.