Impartial avoidance and achievement games for generating symmetric and alternating groups

Authors

Bret J. Benesh, College of Saint Benedict/Saint John's UniversityFollow
Dana C. Ernst
Nándor Sieben

Document Type

Article

Publication Date

7-2016

Disciplines

Algebra | Discrete Mathematics and Combinatorics | Mathematics

Abstract

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 second game. We determine the nim-numbers, and therefore the outcomes, of these games for symmetric and alternating groups.

Copyright Statement

Creative Commons License CC-BY

Recommended Citation

Benesh BJ, Ernst DC, Sieber N. 2016. Impartial avoidance and achievement games for generating symmetric and alternating groups. International Electronic Journal of Algebra 20: 70-85.