Abstract
Groups are shown to be special homomorphic images of inverse semigroups that are residually finite (actually: every element has only finitely many elements ⩾
j
-above). This also leads to a new approach to the Burnside problem. These results extend an earlier paper (
J. C. Birget and J. Rhodes,
J. Pure Appl. Algebra
32 (1984)
, 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
J. C. Birget and J. Rhodes,
J. Pure Appl. Algebra
32 (1984)
, 249–287.