Selective screenability in topological groups

We examine the selective screenability property in topological groups. In the metrizable case we also give characterizations of S c ( O nbd , O ) and Smirnov- S c ( O nbd , O ) in terms of the Haver property and finitary Haver property respectively relative to left-invariant metrics. We prove theorems stating conditions under which S c ( O nbd , O ) is preserved by products. Among metrizable groups we characterize the countable dimensional ones by a natural game.