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
Pages
16
From page
70
To page
85
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
Serial Year
2016
Full Text URL
Record number
2600871
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