Recall that S or Sym β«ήβ¬ is the topological group consisting of all Ο± w x permutations of β«ήβ¬ equipped with the natural topology. In Ca Cameron defines an element of S to be cofinitary if it fixes only finitely many Ο± elements of β«,ήβ¬ a subgroup of S to be cofinitary if all its elements other Ο± than the identity are cofinitary, and goes on to conjecture: Ε½ . 0.1. Conjecture Cameron . Every closed cofinitary group is locally compact. If true, this would entail that all subgroups of S arising as continuous Ο± images of closed cofinitary groups are locally compact. In this paper it is shown that Cameron's conjecture is false in the following strong sense: 0.2. THEOREM. EΒ¨ery closed subgroup of S is the continuous homomorΟ± phic image of a closed cofinitary group. 1. SOME DEFINITIONS AND EXAMPLES 1.1. DEFINITION. S , the infinite symmetric group, is the group of all Ο± permutations of β«.ήβ¬ This group is given the topology generated by all Γ Ε½ . 4 subbasic open sets of the form g g S : g n s k for n, k g β«.ήβ¬ A subΟ± group G -S is cofinitary if for all g g G Ο± α Ο± n g β«ήβ¬ g n s n Β« αn g β«ήβ¬ g n s n ;