Abstract
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.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 10, pp. 1393–1398, October, 1994.
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Poletskikh, V.M., Shestakov, S.S. On topological groups with weak minimality (maximality) condition for noncompact subgroups. Ukr Math J 46, 1540–1544 (1994). https://doi.org/10.1007/BF01066098
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DOI: https://doi.org/10.1007/BF01066098