On the lattice of subgroups of the lamplighter group

TL;DR

This paper investigates the structure of the subgroup lattice of lamplighter groups and explores the concept of relative gradient rank within these groups.

Contribution

It provides new insights into the subgroup lattice structure and introduces the analysis of relative gradient rank for lamplighter groups.

Findings

Detailed characterization of the subgroup lattice

Introduction of the relative gradient rank concept

New structural results for lamplighter groups

Abstract

The paper is devoted to the study of the lattice of subgroups of the Lamplighter type groups and to the relative gradient rank.