Fitting ideals of Jacobian groups of graphs

TL;DR

This paper investigates the algebraic structure of Jacobian groups of graphs, focusing on Fitting ideals and module-theoretic approaches, especially in the context of coverings and Iwasawa theory.

Contribution

It introduces a study of Fitting ideals of Jacobian groups as modules over group rings and explores infinite coverings and Iwasawa theory for graphs.

Findings

Fitting ideals of Jacobian groups are characterized as modules over group rings.

Analysis of Jacobian groups in infinite coverings extends algebraic understanding.

Module-theoretic approach links graph theory with Iwasawa theory concepts.

Abstract

The Jacobian group of a graph is a finite abelian group through which we can study the graph in an algebraic way. When the graph is a finite abelian covering of another graph, the Jacobian group is equipped with the action of the Galois group. In this paper, we study the Fitting ideal of the Jacobian group as a module over the group ring. We also study the corresponding question for infinite coverings. Additionally, this paper includes module-theoretic approach to Iwasawa theory for graphs.