Impartial avoidance and achievement games for generating symmetric and alternating groups

Bret J. Benesh, Dana C Ernst, Nandor Sieben

Research output: Contribution to journalArticle

3 Scopus citations


Anderson and Harary introduced two impartial games on finite groups. Both games are played by two players who alternately select previously- unselected elements of a finite group. The first player who builds a generating set from the jointly-selected elements wins the first game. The first player who cannot select an element without building a generating set loses the sec- ond game. We determine the nim-numbers, and therefore the outcomes, of these games for symmetric and alternating groups.

Original languageEnglish (US)
Pages (from-to)70-85
Number of pages16
JournalInternational Electronic Journal of Algebra
StatePublished - 2016



  • Alternating group
  • Impartial game
  • Maximal subgroup
  • Symmetric group

ASJC Scopus subject areas

  • Algebra and Number Theory

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