1
Tishreen University, Department Of Mathematics, Latakia, Syria
(Mohammadabobala777@gmail.com)
Abstract :
The aim of this paper is to solve the “ON MY TURF" game over some finite nonabelian groups. Also, it presents the following results:
1-) If G has odd order, and the set F contains the identity element, then the first player A has a winning strategy. If F does not contain the identity, then B has a winning strategy.
2-) If G has an even order with only one element of order two, there is a winning strategy related to set F.
3-) If G has an even order with only three elements of order two which generate a subgroup isomorphic to Z2 × Z2, there is a winning strategy related to the set F.
Keywords :
MT-Game; Finite group; Non-abelian group; Algebraic games.
References :
[1] Babinkostova, L., Cosket, S., Kontradyuk, D., Navert, S., Potter, S., and Scheepers, M., "A study of games over finite groups", Publication at www.researchgate.net, July 2015, Boise State University, pp.(1-3).
[2] Al-Najjar, H., Dabash, M., and Barbara, H., "Create HIM, the Adjusted NIM Game, and Analyses Its Winning Strategy", PHD Thesis, University of Aleppo Press, 2013, pp.20-130.
[3] Haushi, M., "Algebraic Structures", Tishreen University Press, 2004, pp. 112-140.
[4] Selvakumari, K., and Lavanya, S., "Neutrosophic Fuzzy Soft Game", International Journal of Engineering and Technology, Vol. 7, 2018, pp. 667-669.
[5] Benesh, B.J., Ernest, D.C., and Sieben, N., "Impartial Avoidance Games for Generating Finite Groups", North-Western European Journal of Mathematics, 2016, pp.89-103.
[6] Ahmad Dar, Y., and Sharma, Y., "Algebraic Method in Game Theory", International Journal of Multidisciplinary Research and Development, Vol. 4, 2017, pp. 368-372.
[7] Bal, M., and Abobala, M., " On The Representation Of Winning Strategies Of Finite Games By Groups and Neutrosophic Groups", Journal Of Neutrosophic and Fuzzy Systems, 2022.
| Style | # |
|---|---|
| MLA | Mohammad Abobala. "Analyzing on My Turf Game Over Some Finite Non-Abelian Groups." Galoitica: Journal of Mathematical Structures and Applications, Vol. 1, No. 1, 2022 ,PP. 08-11 (Doi : https://doi.org/10.54216/GJMSA.010101) |
| APA | Mohammad Abobala. (2022). Analyzing on My Turf Game Over Some Finite Non-Abelian Groups. Journal of Galoitica: Journal of Mathematical Structures and Applications, 1 ( 1 ), 08-11 (Doi : https://doi.org/10.54216/GJMSA.010101) |
| Chicago | Mohammad Abobala. "Analyzing on My Turf Game Over Some Finite Non-Abelian Groups." Journal of Galoitica: Journal of Mathematical Structures and Applications, 1 no. 1 (2022): 08-11 (Doi : https://doi.org/10.54216/GJMSA.010101) |
| Harvard | Mohammad Abobala. (2022). Analyzing on My Turf Game Over Some Finite Non-Abelian Groups. Journal of Galoitica: Journal of Mathematical Structures and Applications, 1 ( 1 ), 08-11 (Doi : https://doi.org/10.54216/GJMSA.010101) |
| Vancouver | Mohammad Abobala. Analyzing on My Turf Game Over Some Finite Non-Abelian Groups. Journal of Galoitica: Journal of Mathematical Structures and Applications, (2022); 1 ( 1 ): 08-11 (Doi : https://doi.org/10.54216/GJMSA.010101) |
| IEEE | Mohammad Abobala, Analyzing on My Turf Game Over Some Finite Non-Abelian Groups, Journal of Galoitica: Journal of Mathematical Structures and Applications, Vol. 1 , No. 1 , (2022) : 08-11 (Doi : https://doi.org/10.54216/GJMSA.010101) |