Collins Russian Dictionary 2nd Edition © HarperCollins Publishers 2000, 1997:
major [ˈmeɪdʒər] n (MIL) майо́р
adj (important) гла́вный; (MUS) мажо́рный
vi (US) (SCOL)
to major in специализи́роваться (impf/perf) в +prp
a major operation (also fig) кру́пная опера́ция
* is used to mark translations which have irregular inflections. The Russian-English side of the dictionary gives inflectional information.