Periodic elements of the free idempotent generated semigroup on a biordered set

TL;DR

This paper proves that all periodic elements in a certain algebraic structure called the free idempotent generated semigroup on any biordered set are contained within subgroups, clarifying their algebraic nature.

Contribution

It establishes that every periodic element in this semigroup context belongs to a subgroup, extending understanding of its algebraic structure.

Findings

Periodic elements belong to subgroups

All periodic elements are contained within subgroups

Clarifies the structure of free idempotent generated semigroups

Abstract

We show that every periodic element of the free idempotent generated semigroup on an arbitrary biordered set belongs to a subgroup of the semigroup.