Locally normal subgroups and ends of locally compact Kac-Moody groups

A locally normal subgroup in a topological group is a subgroup whose normalizer is open. In this paper, we provide a detailed description of the large-scale structure of closed locally normal subgroups of complete Kac-Moody groups over finite fields. Combining that description with the main result from [7], we show that, under mild assumptions, if the Kac- Moody group is one-ended (a property that is easily determined from the generalized Cartan matrix), then it is locally indecomposable, which means that no open subgroup decomposes as a nontrivial direct product.