Synonyms for Dominance (same or very similar meaning)
WordNet sense 1 (the state that exists when one person or group has power over another):
ascendance, ascendancy, ascendency, control, ascendenceWordNet sense 2 (the power or right to give orders or make decisions):
authority, authorization, potency, say-so, authorisationWordNet sense 3 (superior development of one side of the body):
lateralityFrom the ODE community, based on WordNetadd/edit