Gallai’s theorem, an n n -dimensional generalization of Van der Waerden’s theorem on arithmetic progression, is used to prove the following theorem: Let F F be a field and G ⊆ F ∗ G \subseteq {F^ * } a subgroup of finite index n n . There is a positive integer N N , which depends only on n n , so that if Char F = 0 {\text {Char}}F = 0 or Char F ≥ N {\text {Char}}F \geq N , then G − G = F G - G = F .