论文标题
迈向$ C_P \ Times C_P $的增压理论的分类
Toward a Classification of the Supercharacter Theories of $C_p\times C_p$
论文作者
论文摘要
在本文中，我们研究了基本Abelian $ p $ - 订单$ p^2 $的SuperSharacter Theories。我们表明，可以从直接产品建设和$ \ ast $ - 产品建设中产生的增压器理论，可以从自动形态学中获得。我们还证明，任何具有$ 1 $的非身份超级类别或非原理线性辐射量的非身份超级类的订单$ p^2 $的增压器理论都必须来自$ \ ast $ propoduct $ \ ast $ - 产品或直接产品。尽管我们无法证明通用素数的结果，但我们确实在$ p = 2、3、5 $的情况下计算所有的增压特性理论，并基于这些计算以及对较大素数的特定计算，我们为一般的Prime Prime P $做出了几种猜想。
In this paper, we study the superscharacter theories of elementary abelian $p$-groups of order $p^2$. We show that the supercharacter theories that arise from the direct product construction and the $\ast$-product construction can be obtained from automorphisms. We also prove that any supercharacter theory of an elementary abelian $p$-group of order $p^2$ that has a nonidentity superclass of size $1$ or a nonprincipal linear supercharacter must come from either a $\ast$-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 $p$.
