  We provide examples of groups which are indecomposable by direct product, and
more generally which are uniquely decomposable in direct products of
indecomposable groups. Examples include Coxeter groups, for which we give an
alternative approach to recent results of L. Paris.
  For a finitely generated linear group Gamma, we establish an upper bound on
the number of factors of which Gamma can be the direct product. If Gamma is
moreover torsion-free, it follows that Gamma is uniquely decomposable in direct
product of indecomposable groups.
