Topological loops having decomposable solvable multiplication group
Group Theory
2020-12-17 v2
Abstract
In this paper we deal with the class C of decomposable solvable Lie groups having dimension at most six. We determine those Lie groups in C and their subgroups which are the multiplication group Mult(L) and the inner mapping group Inn(L) for three-dimensional connected simply connected topological loops L. These loops L have one- or two-dimensional centre and their group Mult(L) has two- or three-dimensional commutator subgroup. Together with this result we obtain that every at most 3-dimensional connected topological proper loop having a solvable Lie group of dimension at most six as its multiplication group is centrally nilpotent of class two.
Keywords
Cite
@article{arxiv.1507.00638,
title = {Topological loops having decomposable solvable multiplication group},
author = {Ameer Al-Abayechi and Ágota Figula},
journal= {arXiv preprint arXiv:1507.00638},
year = {2020}
}