Collocations for dominance - noun

clear, complete, overwhelming, total | growing, increasing | cultural, economic, military, political, territorial | market | male

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

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

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

~ in
black American dominance in heavyweight boxing

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