On Differential Equations with the Group Property

The purpose of the present work is the discussion of the possible types of homogeneous linear differential equations of which the solutions generate continuous groups of transformations in a space of n dimensions. The geometrical interpretations of the results form perhaps the sole interesting element in a tedious formal presentation. A more elegant form of reasoning is greatly to be wished for, but seems to be impossible at present. The entire paper considers problems inverse to the usual discussions of continuous groups of deformation of a space into itself.