From idempotent-generated semigroups to 2-complexes
by
John Meakin
University of Nebraska

In 1973 Nambooripad introduced the notion of a biordered set as an axiomatic characterization of the set of idempotents of a semigroup relative to certain basic products. By associating a 2-complex with a biorderd set in a natural way, we are able to prove that every finitely presented group arises as a maximal subgroup of the free idempotent-generated semigroup on a finite biordered set, thus disproving a conjecture of Easdown about the structure of these groups. It follows that the word problem for the free idempotent-generated semigroup on a finite biordered set is undecidable.

Date received: January 23, 2006