What Does It Mean?

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From our dictionary:
he•gem•o•ny

(hi•jem'u•nE, hej'u•mO"nE),
n.,
pl. -nies.
1. leadership or predominant influence exercised by one nation over others, as in a confederation.
2. leadership; predominance.
3. (esp. among smaller nations) aggression or expansionism by large nations in an effort to achieve world domination.