Impartial achievement games for generating nilpotent groups
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2018
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| _version_ | 1866916118562603008 |
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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 game introduced by Anderson and Harary. The game is played by two players who alternately choose previously-unselected elements of a finite group. The first player who builds a generating set from the jointly-selected elements wins. We determine the nim-numbers of this game for finite groups of the form $T \times H$, where $T$ is a $2$-group and $H$ is a group of odd order. This includes all nilpotent and hence abelian groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1805_01409 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Impartial achievement games for generating nilpotent groups Benesh, Bret J. Ernst, Dana C. Sieben, Nandor Group Theory Combinatorics 91A46, 20D30 We study an impartial game introduced by Anderson and Harary. The game is played by two players who alternately choose previously-unselected elements of a finite group. The first player who builds a generating set from the jointly-selected elements wins. We determine the nim-numbers of this game for finite groups of the form $T \times H$, where $T$ is a $2$-group and $H$ is a group of odd order. This includes all nilpotent and hence abelian groups. |
| title | Impartial achievement games for generating nilpotent groups |
| topic | Group Theory Combinatorics 91A46, 20D30 |
| url | https://arxiv.org/abs/1805.01409 |