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иметь влияние stresses
gen.	awe; bias; pass upon; prevail on; prevail upon; prevail with; win; catch hold of (на кого-л.); catch hold on (на кого-л.); catch hold over (на кого-л.); catch hold upon (на кого-л.); get hold of (на кого-л.); get hold on (на кого-л.); get hold over (на кого-л.); get hold upon (на кого-л.); have a hold over (sb., на кого-л.); lay hold of (на кого-л.); lay hold on (на кого-л.); lay hold over (на кого-л.); lay hold upon (на кого-л.); seize hold of (на кого-л.); seize hold on (на кого-л.); seize hold over (на кого-л.); seize hold upon (на кого-л.); take hold of (на кого-л.); take hold on (на кого-л.); take hold over (на кого-л.); take hold upon (на кого-л.); dominate (на кого-либо); sway (на кого-либо, что-либо); carry authority; carry weight; be influential with (на кого-либо); have an influence over (на кого-либо); have a bearing on (на что-либо); have influence on (на тж. см. have pull Taras); have the say-so; reign; have the ear of (someone – на кого-либо bookworm); be influential with (someone – на кого-либо)
busin.	have an impact on (smth, на что-л.)
dipl.	sway (на кого-либо что-либо)
idiom.	hold cards (shergilov)
Makarov.	have an influence on (someone – на кого-либо); have an influence upon (someone – на кого-либо); carry impact; bear influence; have effect; have impact; have influence; have an influence over (someone – на кого-либо); wield influence
math.	have a bearing on
nautic.	sway
proj.manag.	have a sway (Kenan Shikhlinsky)
slang	have a say (khanna13)
иметь влияние на кого-либо
Makarov.	have a firm hold over (someone)

иметь влияние: 87 phrases in 18 subjects

American usage, not spelling	1
Astrology	1
Business	4
Diplomacy	3
Finances	1
General	32
Idiomatic	1
Makarov	24
Mass media	3
Mathematics	6
Obsolete / dated	1
Oil and gas	1
Politics	2
SAP tech.	1
Scientific	2
Slang	2
Technology	1
Uncommon / rare	1