Year: 2014
Type: article
Abstract: The conjugacy growth function counts the number of distinct conjugacy classes in a ball of radius n. We give a lower bound for the conjugacy growth of certain branch groups, among them the Grigorchuk group. This bound is a function of intermediate growth. We further prove that certain branch groups have the property that every element can be expressed as a product of uniformly boundedly many conjugates of the generators. We call this property bounded conjugacy width. We also show how bounded conjugacy width relates to other algebraic properties of groups and apply these results to study the palindromic width of some branch groups.
Author: Elisabeth Fink
Institution: Département de mathématiques et applications
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1978314205