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arXiv · 1506.07105

Impartial avoidance games for generating finite groups

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

We study an impartial avoidance game introduced by Anderson and Harary. The game is played by two players who alternately select previously unselected elements of a finite group. The first player who cannot select an element without making the set of jointly-selected elements into a generating set for the group loses the game. We develop criteria on the maximal subgroups that determine the nim-numbers of these games and use our criteria to study our game for several families of groups, including nilpotent, sporadic, and symmetric groups.

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Bret J. Benesh, Dana C. Ernst, Nandor Sieben. 2016-02-01. Impartial avoidance games for generating finite groups. https://arxiv.org/abs/1506.07105

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