Pseudocompact and precompact topological subsemigroups of topological groups.

It is known that every pseudocompact topological group is precompact, we extend this result to a class of subsemigroup of topological groups. Then we use this results to prove that cancellative locally compact countably compact topological semigroups with open shifts are topological groups and to give a sufficient condition under which a locally compact mono- thetic topological semigroup is a compact topological group. [ABSTRACT FROM AUTHOR]