On the dimensions of commutative subalgebras and subgroups
  We consider the functions that bound the dimensions of finite-dimensional associative or Lie algebras in terms of the dimensions of their commutative subalgebras. It is proved that these functions have quadratic growth. As a result, we also get similar estimates for the dimension of a Lie group with bounded dimensions of its abelian Lie subgroups. 
Maria V. Milentyeva
math.RA