Analyzing on My Turf Game Over Some Finite Non-Abelian Groups

Mohammad

doi:https://doi.org/10.54216/GJMSA.010101

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Volume 1 • Issue 1 • PP: 08-11 • 2022

Analyzing on My Turf Game Over Some Finite Non-Abelian Groups

Mohammad Abobala ^1*

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¹Tishreen University, Department Of Mathematics, Latakia, Syria

* Corresponding Author.

DOI https://doi.org/10.54216/GJMSA.010101

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Received: March 10, 2022 Accepted: April 13, 2022

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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.

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Abobala, Mohammad. "Analyzing on My Turf Game Over Some Finite Non-Abelian Groups." Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 1, no. Issue 1, 2022, pp. 08-11. DOI: https://doi.org/10.54216/GJMSA.010101

Abobala, M. (2022). Analyzing on My Turf Game Over Some Finite Non-Abelian Groups. Galoitica: Journal of Mathematical Structures and Applications, Volume 1(Issue 1), 08-11. DOI: https://doi.org/10.54216/GJMSA.010101

Abobala, Mohammad. "Analyzing on My Turf Game Over Some Finite Non-Abelian Groups." Galoitica: Journal of Mathematical Structures and Applications Volume 1, no. Issue 1 (2022): 08-11. DOI: https://doi.org/10.54216/GJMSA.010101

Abobala, M. (2022) 'Analyzing on My Turf Game Over Some Finite Non-Abelian Groups', Galoitica: Journal of Mathematical Structures and Applications, Volume 1(Issue 1), pp. 08-11. DOI: https://doi.org/10.54216/GJMSA.010101

Abobala M. Analyzing on My Turf Game Over Some Finite Non-Abelian Groups. Galoitica: Journal of Mathematical Structures and Applications. 2022;Volume 1(Issue 1):08-11. DOI: https://doi.org/10.54216/GJMSA.010101

M. Abobala, "Analyzing on My Turf Game Over Some Finite Non-Abelian Groups," Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 1, no. Issue 1, pp. 08-11, 2022. DOI: https://doi.org/10.54216/GJMSA.010101

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