Topological loops with solvable multiplication groups of dimension at most six are centrally nilpotent
Publish place: International Journal of Group Theory، Vol: 9، Issue: 2
Publish Year: 1399
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_THEGR-9-2_003
تاریخ نمایه سازی: 14 اردیبهشت 1400
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 $\le ۳$ 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
Authors
Agota Figula
Institute of Mathematics, University of Debrecen, Debrecen, Hungary
Ameer Al-Abayechi
Institute of Mathematics, University of Debrecen, Debrecen, Hungary