The Collaborative International Dictionary of English v.0.48:

Brigadier general \Brig`a*dier" gen"er*al\ [F. brigadier, fr.
   brigade.] (Mil.)
   An officer in rank next above a colonel, and below a major
   general. He commands a brigade, and is sometimes called, by a
   shortening of his title, simple a brigadier.
   [1913 Webster]

WordNet (r) 3.0 (2006):

brigadier general
    n 1: a general officer ranking below a major general [syn:
         brigadier, brigadier general]