Impartial avoidance games for generating finite groups
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2015
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| _version_ | 1866910323253968896 |
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| author | Benesh, Bret J. Ernst, Dana C. Sieben, Nandor |
| author_facet | Benesh, Bret J. Ernst, Dana C. Sieben, Nandor |
| contents | We study an impartial avoidance game introduced by Anderson and Harary. The game is played by two players who alternately select previously unselected elements of a finite group. The first player who cannot select an element without making the set of jointly-selected elements into a generating set for the group loses the game. We develop criteria on the maximal subgroups that determine the nim-numbers of these games and use our criteria to study our game for several families of groups, including nilpotent, sporadic, and symmetric groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1506_07105 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Impartial avoidance games for generating finite groups Benesh, Bret J. Ernst, Dana C. Sieben, Nandor Combinatorics Group Theory 91A46, 20D30 We study an impartial avoidance game introduced by Anderson and Harary. The game is played by two players who alternately select previously unselected elements of a finite group. The first player who cannot select an element without making the set of jointly-selected elements into a generating set for the group loses the game. We develop criteria on the maximal subgroups that determine the nim-numbers of these games and use our criteria to study our game for several families of groups, including nilpotent, sporadic, and symmetric groups. |
| title | Impartial avoidance games for generating finite groups |
| topic | Combinatorics Group Theory 91A46, 20D30 |
| url | https://arxiv.org/abs/1506.07105 |