Supplements on the theory of exponential Lie groups (Q1398165)

The author presents new results in the theory of exponential Lie groups, i.e., Lie groups with surjective exponential function. An additional criterion for Mal'cev splittable exponential Lie groups is presented as well as an additional necessary condition for solvable exponential Lie groups. The author introduces an example of an exponential simple Lie group which is not isomorphic to a linear group. The paper contains an investigation into the role of maximal compactly embedded subgroups of solvable Lie groups with respect to exponentiality. Some results for the general case are also presented and finally two examples are given which show that the problem of exponentiality is rather complex.