Generation of infinite factorizable inverse monoids. (Q444663)

Let \(M\) be an inverse monoid, \(E\) its semilattice of idempotents and \(G\) its group of units. Then \(GE\) is a submonoid of \(M\) called the `factorizable part' of \(M\). The paper under review studies the factorizable parts for the symmetric inverse monoid and the dual symmetric inverse monoid on an infinite set. The author computes the rank (i.e. the minimal cardinality for a generating set), the relative rank related to the group of units, and the Sierpiński rank for these two monoids. Finally, it is shown that neither of these monoids has the semigroup Bergman property (having this property means that for any generating set the length function on the semigroup is bounded).