Group theory via global semigroup theory

Groups are shown to be special homomorphic images of inverse semigroups that are residually finite (actually: every element has only finitely many elements -above). This also leads to a new approach to the Burnside problem. These results extend an earlier paper ([1.], 249–287), but can be read independently. Our goal here is not so much to prove theorems about inverse semigroups as to demonstrate the usefulness of the constructions of [1.], 249–287.