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

Mohammad Abobala

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

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

Mohammad Abobala ^{1
*}

1 Tishreen University, Department Of Mathematics, Latakia, Syria - (Mohammadabobala777@gmail.com)

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

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

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.

Cite This Article As :

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

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

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