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arXiv · 1508.03419

Impartial avoidance and achievement games for generating symmetric and alternating groups

Bret J. Benesh·Dana C. Ernst·Nandor Sieben
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Abstract

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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Bret J. Benesh, Dana C. Ernst, Nandor Sieben. 2015-08-14. Impartial avoidance and achievement games for generating symmetric and alternating groups. https://arxiv.org/abs/1508.03419

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