Finitary shadows of compact subgroups of S(omega )

Abstract

Let LF be the lattice of all subgroups of the group SF(omega ) of all finitary permutations of the set of natural numbers. We consider subgroups of SF(omega ) of the form Ccap SF(omega ), where C is a compact subgroup of the group of all permutations. In particular, we study their distribution among elements of LF. We measure this using natural relations of orthogonality and almost containedness. We also study complexity of the corresponding families of compact subgroups of S(omega ).