The Collaborative International Dictionary of English v.0.48:

Dominance \Dom"i*nance\, Dominancy \Dom"i*nan*cy\, n.
   Predominance; ascendency; authority.
   [1913 Webster]

WordNet (r) 3.0 (2006):

dominance
    n 1: superior development of one side of the body [syn:
         laterality, dominance]
    2: the state that exists when one person or group has power over
       another; "her apparent dominance of her husband was really
       her attempt to make him pay attention to her" [syn:
       dominance, ascendance, ascendence, ascendancy,
       ascendency, control]
    3: the organic phenomenon in which one of a pair of alleles
       present in a genotype is expressed in the phenotype and the
       other allele of the pair is not
    4: the power or right to give orders or make decisions; "he has
       the authority to issue warrants"; "deputies are given
       authorization to make arrests"; "a place of potency in the
       state" [syn: authority, authorization, authorisation,
       potency, dominance, say-so]

Moby Thesaurus II by Grady Ward, 1.0:

66 Moby Thesaurus words for "dominance":
   ascendance, ascendancy, authority, balance of power, charisma,
   charm, clout, consequence, control, credit, dominancy, domination,
   dominion, effect, eminence, eminent domain, enchantment, esteem,
   favor, force, good feeling, hold, importance, incidental power,
   influence, influentiality, insinuation, leadership, leverage,
   magnetism, masterdom, mastery, moment, overlordship, personality,
   persuasion, potency, power, predominance, predominancy,
   predomination, preeminence, preponderance, prepotence, prepotency,
   pressure, prestige, primacy, principality, purchase, reign, repute,
   rule, say, sovereignty, suasion, subtle influence, suggestion,
   superiority, supremacy, suzerainship, suzerainty, sway, upper hand,
   weight, whip hand