Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three-person impartial avoidance games for generating finite cyclic,
  dihedral, and nilpotent groups   We study a three-player variation of the impartial avoidance game introduced
by Anderson and Harary. Three players take turns selecting
previously-unselected elements of a finite group. The losing player is the one
who selects an element that causes the set of jointly-selected elements to be a
generating set for the group, with the previous player winning and the
remaining player coming in second place. We describe the winning strategy for
these games on cyclic, dihedral, and nilpotent groups.

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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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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: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys