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arXiv · 1805.01409

Impartial achievement games for generating nilpotent groups

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

We study an impartial game introduced by Anderson and Harary. The game is played by two players who alternately choose previously-unselected elements of a finite group. The first player who builds a generating set from the jointly-selected elements wins. We determine the nim-numbers of this game for finite groups of the form $T \times H$, where $T$ is a $2$-group and $H$ is a group of odd order. This includes all nilpotent and hence abelian groups.

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Bret J. Benesh, Dana C. Ernst, Nandor Sieben. 2018-05-03. Impartial achievement games for generating nilpotent groups. https://arxiv.org/abs/1805.01409

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