TOPOLOGICAL LOOPS WITH SOLVABLE MULTIPLICATION GROUPS OF DIMENSION AT MOST SIX ARE CENTRALLY NILPOTENT

被引：2

作者：

Figula, Agota ^{[1
]}

Al-Abayechi, Ameer ^{[1
,2
]}

机构：

[1] Univ Debrecen, Inst Math, POBox 400, Debrecen, Hungary

[2] Univ Debrecen, Doctoral Sch Math & Computat Sci, Debrecen, Hungary

来源：

INTERNATIONAL JOURNAL OF GROUP THEORY | 2020年 / 9卷 / 02期

关键词：

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

D O I：

10.22108/ijgt.2019.114770.1522

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 <= 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.

引用

页码：81 / 94

页数：14