Grigorchuk's group of intermediate growth can be represented, through its action on the infinite binary rooted tree, as the automorphism group of a regular ...

We address a question of Grigorchuk by providing both a system of recursive formulas and an asymptotic result for the portrait growth of the first Grigorchuk ...

Grigorchuk's group of intermediate growth can be represented, through its action on the infinite binary rooted tree, as the automorphism group of a regular ...

Grigorchuk's group of intermediate growth can be represented, through its action on the infinite binary rooted tree, as the automorphism group of a regular ...

Grigorchuk's group is a group which acts on the infinite binary tree. It is a permutation representation of \(\Gamma\), and thus generates a map \(\mathcal G\).

Abstract. The Grigorchuk group was first constructed in 1980 by Rostislav. Grigorchuk, defined as a set of measure-preserving maps on the unit interval.

In this dissertation, we construct and investigate a family of groups, indexed by sequences of three symbols, that generalize the famous Grigorchuk's ...

Aug 15, 2008 · Since g /∈ N, the quotient map f : G → G \ N takes G to a finite set G \ N and maps g to a nontrivial element. Thus G is residually finite.

Julia sets of such maps provide an unending supply of self- similar subsets of the complex plane. For example, the Julia set of the quadratic map z 7→ z2 − 1 is ...

Abstract. Let G be the first Grigorchuk group. We show that the commutator width of G is 2: every element g 2 ŒG; G is a product of two commutators, ...