The rank and generating set for inverse limits of wreath products of Abelian groups

摘要

We derive an exact formula for the topological rank d(W) of the inverse limit W =...,A_2,A_1 of iterated wreath products of arbitrary nontrivial finite Abelian groups. By using the language of automorphisms of a spherically homogeneous rooted tree, we construct and study a topological generating set for W with cardinality d(A_1)+ρ~′, where ρ~′ is the topological rank of the profinite Abelian group A_2× A_2×.... In particular, if the group A_1 is cyclic, this approach gives a minimal generating set for W.