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


Brett McElwee


Research Report 2001-14
Date: 27 November 2001


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


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