Write SQL query to solve given problem: List the group name has the most downloaded that have released jazz genres from 1982 or later.. Keep the solution inside sql tag ```sql [SQL-Query] ```
SELECT T1.groupName FROM torrents AS T1 INNER JOIN tags AS T2 ON T1.id = T2.id WHERE T2.tag = 'jazz' AND T1.groupYear >= 1982 ORDER BY T1.totalSnatched DESC LIMIT 1