Abstract :
For any connected Lie group G, we introduce the notion of exponential radical Exp(G) that is the set of all strictly exponentially distorted elements of G. In case G is a connected simply-connected solvable Lie group, we prove that Exp(G) is a connected normal Lie subgroup in G and the exponential radical of the quotient group G/Exp(G) is trivial. Using this result, we show that the relative growth function of any subgroup in a polycyclic group is either polynomial or exponential.
