...an attempt by each group to establish dominance over the other. [+ of/over]

各个小组都想要控制其他小组的企图

These economies will no doubt maintain their dominance of financial markets.

这些经济制度将毫无疑问地维持他们在金融市场上的主导权。

Legislation is the only route to ending the car's dominance as a form of transport.

立法是终止汽车作为主导交通工具的唯一途径。