From this it is easy to see that the isotropy group of our null electrovacuum includes rotations about the e → → 3 axis; two further generators are the two parabolic Lorentz transformations aligned with the e → → 3 direction given in the article on the Lorentz group. In other words, the isotropy group of any null electrovacuum is a three-dimensional Lie group isomorphic to E(2), the isometry group of the euclidean plane.