  For a Polish group G let cov_G be the minimal number of translates of a fixed
closed nowhere dense subset of G required to cover G. For many locally compact
G this cardinal is known to be consistently larger than cov(meager) which is
the smallest cardinality of a covering of the real line by meagre sets. It is
shown that for several non-locally compact groups cov_G=cov(meager). For
example the equality holds for the group of permutations of the integers, the
additive group of a separable Banach space with an unconditional basis and the
group of homeomorphisms of various compact spaces.
  Most recent version at: www.math.wisc.edu/~miller
