University of IsfahanInternational Journal of Group Theory2251-76509220200601Topological loops with solvable multiplication groups of dimension at most six are centrally nilpotent81942351110.22108/ijgt.2019.114770.1522ENAgotaFigulaInstitute of Mathematics, University of Debrecen, Debrecen, HungaryAmeerAl-AbayechiInstitute of Mathematics, University of Debrecen, Debrecen, HungaryJournal Article20181228The main result of our consideration is the proof of the centrally nilpotency of class two property for connected topological proper loops $L$ of dimension $\le 3$ which have an at most six-dimensional solvable indecomposable Lie group as their multiplication group. This theorem is obtained from our previous classification by the investigation of six-dimensional indecomposable solvable multiplication Lie groups having a five-dimensional nilradical. We determine the Lie algebras of these multiplication groups and the subalgebras of the corresponding inner mapping groups.https://ijgt.ui.ac.ir/article_23511_9f0b68dcbecfb72da78de4a261cbfbd0.pdf