The Polycyclic Monoids P n and the Thompson Groups V n,1

Abstract

We construct what we call the strong orthogonal completion C n of the polycyclic monoid P n on n generators. The inverse monoid C n is congruence free and its group of units is the Thompson group V n,1. Copies of C n can be constructed from partitions of sets into n blocks each block having the same cardinality as the underlying set.