Document Type : Ischia Group Theory 2018

**Authors**

Institute of Mathematics, University of Debrecen, Debrecen, Hungary

**Abstract**

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.

**Keywords**

- Multiplication group and inner mapping group of topological loops
- topological transformation group
- solvable Lie algebras
- centrally nilpotent loops

**Main Subjects**

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Proceedings of the Ischia Group Theory 2018- Part 2

June 2020Pages 81-94

**Receive Date:**28 December 2018**Revise Date:**13 March 2019**Accept Date:**28 March 2019**Published Online:**01 June 2020