IMPARTIAL AVOIDANCE AND ACHIEVEMENT GAMES FOR GENERATING SYMMETRIC AND ALTERNATING GROUPS
Bret J. Benesh, Dana C. Ernst, Nándor Sieben · International Electronic Journal of Algebra · 2016
Anderson and Harary introduced two impartial games on finite groups. Both games are played by two players who alternately select previouslyunselected 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 second game. We determine the nim-numbers, and therefore the outcomes, of these games for symmetric and alternating groups.