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## IMPARTIAL AVOIDANCE AND ACHIEVEMENT GAMES FOR GENERATING SYMMETRIC AND ALTERNATING GROUPS

#### Bret J. Benesh [1] , Dana C. Ernst [2] , Nandor Sieben [3]

##### 236 193

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.
Impartial game, maximal subgroup, symmetric group, alternating group
Konular Matematik JA95MN24AT Makaleler Yazar: Bret J. Benesh Yazar: Dana C. Ernst Yazar: Nandor Sieben
 Bibtex @ { ieja266184, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2016}, volume = {20}, pages = {70 - 85}, doi = {10.24330/ieja.266184}, title = {IMPARTIAL AVOIDANCE AND ACHIEVEMENT GAMES FOR GENERATING SYMMETRIC AND ALTERNATING GROUPS}, key = {cite}, author = {Sieben, Nandor and Ernst, Dana C. and Benesh, Bret J.} } APA Benesh, B , Ernst, D , Sieben, N . (2016). IMPARTIAL AVOIDANCE AND ACHIEVEMENT GAMES FOR GENERATING SYMMETRIC AND ALTERNATING GROUPS. International Electronic Journal of Algebra, 20 (20), 70-85. DOI: 10.24330/ieja.266184 MLA Benesh, B , Ernst, D , Sieben, N . "IMPARTIAL AVOIDANCE AND ACHIEVEMENT GAMES FOR GENERATING SYMMETRIC AND ALTERNATING GROUPS". International Electronic Journal of Algebra 20 (2016): 70-85 Chicago Benesh, B , Ernst, D , Sieben, N . "IMPARTIAL AVOIDANCE AND ACHIEVEMENT GAMES FOR GENERATING SYMMETRIC AND ALTERNATING GROUPS". International Electronic Journal of Algebra 20 (2016): 70-85 RIS TY - JOUR T1 - IMPARTIAL AVOIDANCE AND ACHIEVEMENT GAMES FOR GENERATING SYMMETRIC AND ALTERNATING GROUPS AU - Bret J. Benesh , Dana C. Ernst , Nandor Sieben Y1 - 2016 PY - 2016 N1 - doi: 10.24330/ieja.266184 DO - 10.24330/ieja.266184 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 70 EP - 85 VL - 20 IS - 20 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.266184 UR - http://dx.doi.org/10.24330/ieja.266184 Y2 - 2019 ER - EndNote %0 International Electronic Journal of Algebra IMPARTIAL AVOIDANCE AND ACHIEVEMENT GAMES FOR GENERATING SYMMETRIC AND ALTERNATING GROUPS %A Bret J. Benesh , Dana C. Ernst , Nandor Sieben %T IMPARTIAL AVOIDANCE AND ACHIEVEMENT GAMES FOR GENERATING SYMMETRIC AND ALTERNATING GROUPS %D 2016 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 20 %N 20 %R doi: 10.24330/ieja.266184 %U 10.24330/ieja.266184 ISNAD Benesh, Bret J. , Ernst, Dana C. , Sieben, Nandor . "IMPARTIAL AVOIDANCE AND ACHIEVEMENT GAMES FOR GENERATING SYMMETRIC AND ALTERNATING GROUPS". International Electronic Journal of Algebra 20 / 20 (Aralık 2016): 70-85. http://dx.doi.org/10.24330/ieja.266184