Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Piecewise excluding geodesic languages   The complexity of a geodesic language has connections to algebraic properties
of the group. Gilman, Hermiller, Holt, and Rees show that a finitely generated
group is virtually free if and only if its geodesic language is locally
excluding for some finite inverse-closed generating set. The existence of such
a correspondence and the result of Hermiller, Holt, and Rees that finitely
generated abelian groups have piecewise excluding geodesic language for all
finite inverse-closed generating sets motivated our work. We show that a
finitely generated group with piecewise excluding geodesic language need not be
abelian and give a class of infinite non-abelian groups which have piecewise
excluding geodesic languages for certain generating sets. The quaternion group
is shown to be the only non-abelian 2-generator group with piecewise excluding
geodesic language for all finite inverse-closed generating sets. We also show
that there are virtually abelian groups with geodesic languages which are not
piecewise excluding for any finite inverse-closed generating set.

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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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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: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio