IMPARTIAL AVOIDANCE AND ACHIEVEMENT GAMES FOR GENERATING SYMMETRIC AND ALTERNATING GROUPS

Year 2016, Volume: 20 Issue: 20, 70 - 85, 01.12.2016

Bret J. Benesh Dana C. Ernst Nandor Sieben

https://doi.org/10.24330/ieja.266184

Cited By: 4

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