Semigroups and Hilbert's fifth problem
The properties of -factorizable groups and their subgroups are studied. We show that a locally compact group is -factorizable if and only if is -compact. It is proved that a subgroup of an -factorizable group is -factorizable if and only if is -embedded in . Therefore, a subgroup of an -factorizable group need not be -factorizable, and we present a method for constructing non--factorizable dense subgroups of a special class of -factorizable groups. Finally, we construct a closed...