Impartial achievement games for generating nilpotent groups

Bret J. Benesh, Dana C. Ernst, Nándor Sieben

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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)
Pages (from-to)515-527
Number of pages13
JournalJournal of Group Theory
Issue number3
StatePublished - May 1 2019

ASJC Scopus subject areas

  • Algebra and Number Theory


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