Impartial avoidance and achievement games for generating symmetric and alternating groups
Int. Electron. J. Algebra 20, 70-85, 2016 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...
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Zusammenfassung: | Int. Electron. J. Algebra 20, 70-85, 2016 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. |
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DOI: | 10.48550/arxiv.1508.03419 |