Totally disconnected locally compact groups with just infinite locally normal subgroups

We obtain some global features of totally disconnected locally compact (t.d.l.c.) groups G that are locally isomorphic to a just infinite profinite group, building on an earlier result of Barnea-Ershov-Weigel and also using tools developed by P.-E. Caprace, G. Willis and the author for studying local structure in t.d.l.c. groups. The approach uses the following property of just infinite profinite groups, essentially due to Wilson: given a locally normal subgroup K of G, then there is an open subgroup of K that is a direct factor of an open subgroup of G. This is a local property of t.d.l.c. groups and we obtain a characterization of the local isomorphism types of t.d.l.c. groups that have it.