TY - JOUR
ID - 23511
TI - Topological loops with solvable multiplication groups of dimension at most six are centrally nilpotent
JO - International Journal of Group Theory
JA - IJGT
LA - en
SN - 2251-7650
AU - Figula, Agota
AU - Al-Abayechi, Ameer
AD - Institute of Mathematics, University of Debrecen, Debrecen, Hungary
Y1 - 2020
PY - 2020
VL - 9
IS - 2
SP - 81
EP - 94
KW - Multiplication group and inner mapping group of topological loops
KW - topological transformation group
KW - solvable Lie algebras
KW - centrally nilpotent loops
DO - 10.22108/ijgt.2019.114770.1522
N2 - 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.
UR - https://ijgt.ui.ac.ir/article_23511.html
L1 - https://ijgt.ui.ac.ir/article_23511_9f0b68dcbecfb72da78de4a261cbfbd0.pdf
ER -