Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Impartial avoidance and achievement games for generating symmetric and
  alternating groups   We study two impartial games introduced by Anderson and Harary. Both games
are played by two players who alternately select previously-unselected elements
of a finite group. The first player who builds a generating set from the
jointly-selected elements wins the first game. The first player who cannot
select an element without building a generating set loses the second game. We
determine the nim-numbers, and therefore the outcomes, of these games for
symmetric and alternating groups.

8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas