“Majority-in-Interest” is the same as “controlling majority”, i.e., the majority who have the majority of shares, vs. to majority in numbers. Maybe you could translate it as վերահսկող մեծամասնություն, though there may be a special term for it.

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Note added at 12 hrs (2006-10-25 11:41:04 GMT)
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“majority interest” can be translated as “վերահսկիչ փաթեթ” please see this link: http://www.banks.am/index.php?sub=shownews&newsid=20060705_1 OR “հսկիչ փաթեթ” here’s a link: http://www.azg.am/print_new.php?num=0000000110&lang=AR . So I maybe “վերահսկիչ մեծամասնություն” OR “հսկիչ մեծամասնություն” is better than “վերահսկող մեծամասնություն”

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Note added at 2 days16 hrs (2006-10-27 15:47:32 GMT) Post-grading
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Thank you, Hasmik.