Document Type

Article

Publication Date

7-2016

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.

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