The Immersibility of a Semigroup into a Group
Jim Lambek · Canadian Journal of Mathematics · 1951
A semigroup is a set of elements which is closed under an associative operation, usually called multiplication. When can a semigroup be embedded in a group, i.e., under what condition is it isomorphic to a subset of a group? A necessary condition for immersibility is clearly the so-called cancellation law: