Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conjugacy Growth and Conjugacy Width of Certain Branch Groups   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 proof 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.

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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an