The integer group determinants for the non-abelian groups of order 18

TL;DR

This paper provides a comprehensive analysis of the integer group determinants specifically for the non-abelian groups of order 18, expanding understanding of their algebraic properties.

Contribution

It offers the first complete characterization of integer group determinants for all non-abelian groups of order 18, filling a gap in algebraic number theory.

Findings

Complete description of determinants for these groups

Identification of algebraic properties unique to order 18 groups

Foundation for further research in group determinants

Abstract

We obtain a complete description of the integer group determinants for the non-abelian groups of order 18.