  Methods of Lie group analysis of differential equations are extended to weak
solutions of (linear and nonlinear) PDEs, where the term ``weak solution''
comprises the following settings:
  (a) Distributional solutions. (b) Solutions in generalized function algebras.
(c) Solutions in the sense of association (corresponding to a number of weak or
integral solution concepts in classical analysis).
  Factorization properties and infinitesimal criteria are developed that allow
to treat all three settings simultaneously, thereby unifying and extending
previous work in this area.
