Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Engel elements in some fractal groups   Let $p$ be a prime and let $G$ be a subgroup of a Sylow pro-$p$ subgroup of
the group of automorphisms of the $p$-adic tree. We prove that if $G$ is
fractal and $|G':\mathrm{st}_G(1)'|=\infty$, then the set $L(G)$ of left Engel
elements of $G$ is trivial. This result applies to fractal nonabelian groups
with torsion-free abelianization, for example the Basilica group, the
Brunner-Sidki-Vieira group, and also to the GGS-group with constant defining
vector.
  We further provide two examples showing that neither of the requirements
$|G':\mathrm{st}_G(1)'|=\infty$ and being fractal can be dropped.

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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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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: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph