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