%0 Journal Article
%T Topological loops with solvable multiplication groups of dimension at most six are centrally nilpotent
%J International Journal of Group Theory
%I University of Isfahan
%Z 2251-7650
%A Figula, Agota
%A Al-Abayechi, Ameer
%D 2020
%\ 06/01/2020
%V 9
%N 2
%P 81-94
%! Topological loops with solvable multiplication groups of dimension at most six are centrally nilpotent
%K Multiplication group and inner mapping group of topological loops
%K topological transformation group
%K solvable Lie algebras
%K centrally nilpotent loops
%R 10.22108/ijgt.2019.114770.1522
%X The 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.
%U http://ijgt.ui.ac.ir/article_23511_9f0b68dcbecfb72da78de4a261cbfbd0.pdf