Title of article :
IMPARTIAL AVOIDANCE and ACHIEVEMENT GAMES FOR GENERATING SYMMETRIC and ALTERNATING GROUPS
Author/Authors :
Benesh, Bret Department of Mathematics - College of Saint Benedict and Saint John’s University - College Avenue South, USA , Ernst, Dana Department of Mathematics and Statistics - Northern Arizona University, USA , Sieben, Nandor Department of Mathematics and Statistics - Northern Arizona University, USA
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
Journal title :
International Electronic Journal of Algebra
