  In this paper we give conditions under which a topological semigroup can be
embedded algebraically and topologically into a compact topological group. We
prove that every feebly compact regular first countable cancellative
commutative topological semigroup with open shifts is a topological group, as
well as every connected locally compact Hausdorff cancellative commutative
topological monoid with open shifts. Finally, we use these results to give
sufficient conditions on a topological semigroup that guarantee it to have
countable cellularity.
