Impartial achievement games for generating nilpotent groups

Bret J. Benesh, Dana C Ernst, Nandor Sieben

Research output: Contribution to journalArticle


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.

Original languageEnglish (US)
JournalJournal of Group Theory
StateAccepted/In press - Jan 1 2018

ASJC Scopus subject areas

  • Algebra and Number Theory

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