Cameron's cofinitary group conjecture (Q1383965)

The author shows that Cameron's conjecture about local compactness of cofinitary subgroups of \(S_\infty\) is false. -- Let \(S_\infty\) be the group of all permutations of \(\mathbb{N}\) endowed with pointwise topology. An element of \(S_\infty\) is called cofinitary if it fixes finitely many elements of \(\mathbb{N}\) only. A subgroup of \(S_\infty\) is said to be cofinitary if all of its elements except the identity are cofinitary. The author proves that every closed subgroup of \(S_\infty\) is a continuous homomorphic image of a closed cofinitary subgroup of \(S_\infty\), thus disproving the attractive hypothesis.