# Subgroups of the Free Semigroup on a Biordered Set in Which Principal Ideals are Singletons

## Author

**Brett McElwee**

## Status

Research Report 2001-14

Date: 27 November 2001

## Abstract

Easdown has conjectured that the subgroups of the free semigroup on an
arbitrary biordered set are free. In this note a weaker conjecture is
verified. It is shown that the subgroups of the free semigroup on a biordered
set in which principal ideals are singletons are free. In addition, an
expression is given for the ranks of the maximal subgroups. This generalizes
a result due to Pastijn which involves the free semigroup on a rectangular
biset.

## Key phrases

free subgroups. free semigroup on a biordered set. rank of maximal
subgroups. singleton principal ideals.

## AMS Subject Classification (1991)

Primary: 20M05

Secondary: 06A99

## Content

The paper is available in the following forms:
- TeX dvi format:
- 2001-14.dvi.gz (11kB) or
2001-14.dvi (24kB)

- PostScript:
- 2001-14.ps.gz (104kB) or
2001-14.ps (216kB)

##### To minimize network load, please choose the smaller gzipped .gz form if
and only if your browser client supports it.

Sydney Mathematics and Statistics