Lie algebra associated with the group of finitary automorphisms of p-adic tree

Abstract

We study the Sylow p-subgroup FP ∞ of the finitary automorphism group of the p-adic rooted tree for a prime p > 2 . The fully invariant subgroups of the group FP ∞ are characterized, in particular the lower central series and the Lazard series of FP ∞ are described. This allows us to study the Lie algebra associated with the group FP ∞ and show that it has a special tableau representation. The lower central series, the derived series, and the Engel series of this Lie algebra are described.