Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Subgroup Distortion in Wreath Products of Cyclic Groups   We study the effects of subgroup distortion in the wreath products A wr Z,
where A is finitely generated abelian. We show that every finitely generated
subgroup of A wr Z has distortion function equivalent to some polynomial.
Moreover, for A infinite, and for any polynomial l^k, there is a 2-generated
subgroup of A wr Z having distortion function equivalent to the given
polynomial. Also a formula for the length of elements in arbitrary wreath
product H wr G easily shows that the group Z_2 wr Z^2 has distorted subgroups,
while the lamplighter group Z_2 wr Z has no distorted (finitely generated)
subgroups.

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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph