Abstract. It is well-known that an inverse monoid is factorizable if and only if it is a homomorphic image of a semidirect product of a semilattice (with identity) by a group. We use this structure to describe a presentation of an arbitrary factorizable inverse monoid in terms of presentations of its group of units and semilattice of idempotents, together with some other data. We apply this theory to quickly deduce a well-known presentation of the symmetric inverse monoid on a finite set.

AMS Subject Classification (1991): 20M05, 20M18; 20M20

Keyword(s): Factorizable inverse monoid, presentations, symmetric inverse monoid

Received July 20, 2004, and in revised form June 10, 2005. (Registered under 5885/2009.)