  In this paper we give sufficient conditions under which a subsemigroup of a
topological group is a subgroup, adding to the results given in \cite{Kosh,
can, axioms, forum, Hof, cc, locally} where conditions exist (such as locally
compactness, compactness, feeble compactness and sequential compactness) for a
semigroup to be a group. In our work we proved that closed precompact
subsemigroups of topological groups are semigroups, just like open
pseudocompact monoids of topological groups.
