Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite generation of iterated wreath products   Let $(G_n,X_n)$ be a sequence of finite transitive permutation groups with
uniformly bounded number of generators. We prove that the infinitely iterated
permutational wreath product $...\wr G_2\wr G_1$ is topologically finitely
generated if and only if the profinite abelian group $\prod_{n\geq 1} G_n/G'_n$
is topologically finitely generated. As a corollary, for a finite transitive
group $G$ the minimal number of generators of the wreath power $G\wr...\wr G\wr
G$ ($n$ times) is bounded if $G$ is perfect, and grows linearly if $G$ is
non-perfect. As a by-product we construct a finitely generated branch group,
which has maximal subgroups of infinite index, answering [2,Question 14].

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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an