Topological loops with solvable multiplication groups of dimension at most six are centrally nilpotent
نویسندگان
1 Institute of Mathematics, University of Debrecen, Debrecen, Hungary
2 Institute of Mathematics, University of Debrecen, Debrecen, Hungary
doi
10.22108/ijgt.2019.114770.1522چکیده
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.
