Collocations for dominance - noun

absolute, clear, complete, overwhelming, total
growing, increasing
cultural, economic, military, political, social, territorial
market
male
global, world
the competition for new markets and global dominance

achieve, assert, assume, establish, exert, gain
The company soon achieved complete dominance in the marketplace.

have, maintain, retain
The company is determined to maintain dominance in the market.

demonstrate, show
He had to show his dominance by beating the other men.

challenge, undermine
Ex-colonial countries began to challenge the cultural dominance of Europe.

dominance in
American dominance in heavyweight boxing

dominance over
He asserted his dominance over the other party members.