University of IsfahanInternational Journal of Group Theory2251-765020190328Topological loops with solvable multiplication groups of dimension at most six are centrally nilpotent2351110.22108/ijgt.2019.114770.1522ENAgota FigulaInstitute of Mathematics, University of Debrecen, Debrecen, HungaryAmeer Al-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.http://ijgt.ui.ac.ir/article_23511_a2cb67d2f233db19723ff5524a9540da.pdf