On partitions of groups into dense subsets

It is proved that every countable topological group not containing an open Boolean subgroup can be partitioned into countably many dense subsets. It is also proved that every countable group with finitely many elements of order 2, that can be embedded in a compact topological group, can be partitioned into countably many subsets dense in any nondiscrete group topology. © 2002 Elsevier Science B.V. All rights reserved.