Automorphisms of restricted parabolic trees and Sylow p-subgroups of the finitary symmetric group

In the paper we introduce the notion of a k-adic restricted parabolic tree Dk and investigate the group AutDk of automorphisms of this tree. In particular, we characterize the Sylow p-subgroups in the subgroup AutfDp of finitary automorphisms of a p-adic restricted parabolic tree. Then we use the characterization for the classification of Sylow p-subgroups in the finitary symmetric group FSN.