The discontinuity group of a locally bounded homomorphism of a connected Lie group into a connected Lie group is commutative (Q6052500)

Let \(G\), \(H\) be Lie groups and \(\pi : G \rightarrow H\) be a locally bounded homomorphism. Let \(\mathfrak{U}_{G}\) be the filter of neighborhoods of the identity of \(G\), then the set \(\mathrm{DG}(\pi)=\bigcap_{U \in \mathfrak{U}} \overline{\pi(U)}\) is a subgroup of \(H\) called the discontinuity group of \(\pi\). In the paper under review the author proves not only that \(\mathrm{DG}(\pi)\) is compact and connected (which is known) but also commutative.