On topological groups with weak minimality (maximality) condition for noncompact subgroups - Poletskikh, V. M.; Shestakov, S. S. (Ukrains’kyi Matematychnyi Zhurnal, 1994)
We present the structure of a locally compact solvablep-group satisfying the weak minimality (maximality) condition for noncompact subgroups. As a consequence, we obtain the structure of a locally compact prosolvablep-group satisfying the minimality (maximality) condition for noncompact sub-groups. We also construct an example to demonstrate that these results are not true for arbitrary inductively compact locally compact totally disconnected solvable groups.