Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The spectrum of nim-values for achievement games for generating finite
  groups   We study an impartial achievement game introduced by Anderson and Harary. The
game is played by two players who alternately select previously unselected
elements of a finite group. The game ends when the jointly selected elements
generate the group. The last player able to make a move is the winner of the
game. We prove that the spectrum of nim-values of these games is
$\{0,1,2,3,4\}$. This positively answers two conjectures from a previous paper
by the last two authors.

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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: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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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: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol