A q-player impartial avoidance game for generating finite groups
Abstract We study a q-player variation of the impartial avoidance game introduced by Anderson and Harary, where q is a prime. The game is played by the q players taking turns selecting previously-unselected elements of a finite group. The losing player is the one who selects an elemen...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Berlin Heidelberg
2021
|
| Online Access: | https://hdl.handle.net/1721.1/131441 |
| _version_ | 1826199853525368832 |
|---|---|
| author | Benesh, Bret J Gaetz, Marisa R |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Benesh, Bret J Gaetz, Marisa R |
| author_sort | Benesh, Bret J |
| collection | MIT |
| description | Abstract
We study a q-player variation of the impartial avoidance game introduced by Anderson and Harary, where q is a prime. The game is played by the q players taking turns selecting previously-unselected elements of a finite group. The losing player is the one who selects an element that causes the set of jointly-selected elements to be a generating set for the group, with the previous player winning. We introduce a ranking system for the other players to prevent coalitions. We describe the winning strategy for these games on cyclic, nilpotent, dihedral, and dicyclic groups. |
| first_indexed | 2024-09-23T11:26:50Z |
| format | Article |
| id | mit-1721.1/131441 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:26:50Z |
| publishDate | 2021 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1314412023-02-17T18:55:32Z A q-player impartial avoidance game for generating finite groups Benesh, Bret J Gaetz, Marisa R Massachusetts Institute of Technology. Department of Mathematics Abstract We study a q-player variation of the impartial avoidance game introduced by Anderson and Harary, where q is a prime. The game is played by the q players taking turns selecting previously-unselected elements of a finite group. The losing player is the one who selects an element that causes the set of jointly-selected elements to be a generating set for the group, with the previous player winning. We introduce a ranking system for the other players to prevent coalitions. We describe the winning strategy for these games on cyclic, nilpotent, dihedral, and dicyclic groups. 2021-09-20T17:17:05Z 2021-09-20T17:17:05Z 2018-05-10 2020-09-24T20:45:47Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/131441 en https://doi.org/10.1007/s00182-018-0624-z Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Springer-Verlag GmbH Germany, part of Springer Nature application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Benesh, Bret J Gaetz, Marisa R A q-player impartial avoidance game for generating finite groups |
| title | A q-player impartial avoidance game for generating finite groups |
| title_full | A q-player impartial avoidance game for generating finite groups |
| title_fullStr | A q-player impartial avoidance game for generating finite groups |
| title_full_unstemmed | A q-player impartial avoidance game for generating finite groups |
| title_short | A q-player impartial avoidance game for generating finite groups |
| title_sort | q player impartial avoidance game for generating finite groups |
| url | https://hdl.handle.net/1721.1/131441 |
| work_keys_str_mv | AT beneshbretj aqplayerimpartialavoidancegameforgeneratingfinitegroups AT gaetzmarisar aqplayerimpartialavoidancegameforgeneratingfinitegroups AT beneshbretj qplayerimpartialavoidancegameforgeneratingfinitegroups AT gaetzmarisar qplayerimpartialavoidancegameforgeneratingfinitegroups |