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×H, where T is a 2-group and H is a group of odd order. This includes all nilpotent and hence abelian groups.
© 2019 Walter de Gruyter GmbH, Berlin/Boston. Originally published in Journal of Group Theory, Volume 22, Issue 3, Pages 515–527, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/jgth-2018-0117.
Benesh BJ, Ernst DC, Sieben N. 2019. Impartial achievement games for generating nilpotent groups. Journal of Group Theory 22(3): 515-527.
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