On topological groups with weak minimality (maximality) condition for noncompact subgroups

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.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 10, pp. 1393–1398, October, 1994.