IMPARTIAL AVOIDANCE AND ACHIEVEMENT GAMES FOR GENERATING SYMMETRIC AND ALTERNATING GROUPS

Authors : Bret J Benesh, Dana C Ernst, Nandor Sieben

Pages : 70-85

Doi:10.24330/ieja.266184

View : 12 | Download : 8

Publication Date : 2016-12-01

Article Type : Research Paper

Abstract :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.
Keywords : Impartial game, maximal subgroup, symmetric group, alternating group