Ends for subsemigroups of finite index

TL;DR

This paper investigates the properties of ends in finitely generated semigroups, showing that the number of ends remains invariant under certain finite index subsemigroup conditions.

Contribution

It establishes that the number of ends is preserved for subsemigroups of finite Rees index and finite Green index in cancellative semigroups.

Findings

Number of ends is preserved under finite Rees index subsemigroups.

Number of ends is preserved under finite Green index subsemigroups in cancellative semigroups.

Provides new invariance results for ends in semigroup theory.

Abstract

In this paper we study ends of finitely generated semigroups. The ends we are working with are the ends of the undirected graphs of Cayley graphs of finitely generated semigroups. We prove that the number of ends is preserved for subsemigroups of finite Rees index, and prove the same result for finite Green index subsemigroups of cancellative semigroups.