An $n$-adic generalization of the Lodha-Moore group

TL;DR

This paper introduces an $n$-adic generalization of the Lodha-Moore group, exploring its properties and similarities with Thompson groups, expanding the understanding of these algebraic structures.

Contribution

It presents a novel $n$-adic generalization of the Lodha-Moore group and analyzes its properties in relation to Thompson groups.

Findings

Established properties of the $n$-adic Lodha-Moore group

Identified analogues with Thompson group $F$ and $F(n)$

Extended the theoretical framework of these groups

Abstract

We generalized the Lodha-Moore group into $n$-adic and showed analogues in the Lodha-Moore group of properties between the Thompson group $F$ and the generalized Thompson group $F(n)$.