Distal Actions of Automorphisms of Lie Groups <i>G</i> on Sub_<i>G</i>

Abstract For a locally compact metrisable group G , we study the action of ${\rm Aut}(G)$ on Sub}_G$ set closed subgroups endowed with Chabauty topology. Given an automorphism T relate distality -action that under certain condition. If is connected Lie group, characterise in terms compactness subgroup generated by conditions center or as follows: has no central positive dimension unipotent contained component identity . Moreover, also show acts distally if and only either it isomorphic to direct product vector group. All results groups mentioned above hold for Sub}^a_G$ subset consisting abelian