Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 10.54216/GJSMA https://www.americaspg.com/journals/show/1302 2022 2022 Tishreen University, Department Of Mathematics, Latakia, Syria Mohammad Abobala 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. 2022 2022 08 11 10.54216/GJMSA.010101 https://www.americaspg.com/articleinfo/33/show/1302