Topological loops with solvable multiplication groups of dimension at most six are centrally nilpotent

Document Type : Ischia Group Theory 2018


Institute of Mathematics, University of Debrecen, Debrecen, Hungary


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.


Main Subjects