On the monomial algebra associated to the monomial characters of a finite group

Abstract

Given a finite group $G$, we study the monomial algebra $R_G$, generated by the monomial characters of $G$. In particular, we note that the integral closure of $R_G$ is contained in the algebra generated by those characters $\chi$ for which their associated Artin L-function $L(s,\chi )$ is holomorphic at $s_0\in \mathbb{C}\setminus \{1\}$. Also, we discuss the supercharacter theoretic case.

12 pages. arXiv admin note: text overlap with arXiv:2106.10953

References in corpus (2)

• A Supercharacter Analogue for Normality
• On supercharacter theoretic generalizations of monomial groups and Artin's conjecture