having hegemony, or dominance: the ruling party's hegemonic control of all facets of society.

Sometimes heg·e·mon·i·cal.
Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2019

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Word Origin and History for hegemonic

1650s, from Greek hegemonikos "related to a leader, capable of command," from hegemon (see hegemony). Earlier in same sense was hegemonical (1610s).

Online Etymology Dictionary, © 2010 Douglas Harper