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On supercharacter theoretic generalizations of monomial groups and Artin's conjecture

Mircea Cimpoeas, Alexandru F. Radu

Abstract

We extend the notions of quasi-monomial groups and almost monomial groups, in the framework of supercharacter theories, and we study their connection with Artin's conjecture regarding the holomorphy of Artin $L$-functions.

On supercharacter theoretic generalizations of monomial groups and Artin's conjecture

Abstract

We extend the notions of quasi-monomial groups and almost monomial groups, in the framework of supercharacter theories, and we study their connection with Artin's conjecture regarding the holomorphy of Artin -functions.

Paper Structure

This paper contains 3 sections, 15 theorems, 43 equations.

Table of Contents

  1. Preliminaries
  2. Supercharacter theoretic quasi and almost monomial groups
  3. Supercharacter theoretic Artin conjecture

Key Result

Proposition 1.3

Let $G$ be a finite group and assume that $\operatorname{Irr}(G)=\{\chi_1,\ldots,\chi_r\}$. Then, the following are equivalent:

Theorems & Definitions (35)

  • Definition 1.1
  • Definition 1.2
  • Proposition 1.3
  • proof
  • Example 1.4
  • Theorem 1.5
  • Theorem 1.6
  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • ...and 25 more