I was reading an article about back ground of Killing's work by Thomas Hawkins from Historia mathematica 1980.In it Hawkin's says that,Killing was trying to generalise all types of space forms-Euclidean as well as non-Euclidean.But to classify he need more analytical tools.So he proved that space forms forms finite dimensional Lie algebra.Surely not in modern version.In this part Hawkins says that infinite motions will commute.But two finite dimensional motions need not commute.
I could not understand this idea of infinitesimal commutativity and .What does it mean ?