
تعداد نشریات | 43 |
تعداد شمارهها | 1,706 |
تعداد مقالات | 13,973 |
تعداد مشاهده مقاله | 33,598,183 |
تعداد دریافت فایل اصل مقاله | 13,323,616 |
Topological loops with solvable multiplication groups of dimension at most six are centrally nilpotent | ||
International Journal of Group Theory | ||
مقاله 3، دوره 9، شماره 2، شهریور 2020، صفحه 81-94 اصل مقاله (232.01 K) | ||
نوع مقاله: Ischia Group Theory 2018 | ||
شناسه دیجیتال (DOI): 10.22108/ijgt.2019.114770.1522 | ||
نویسندگان | ||
Agota Figula* ؛ Ameer Al-Abayechi | ||
Institute of Mathematics, University of Debrecen, Debrecen, Hungary | ||
چکیده | ||
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. | ||
کلیدواژهها | ||
Multiplication group and inner mapping group of topological loops؛ topological transformation group؛ solvable Lie algebras؛ centrally nilpotent loops | ||
مراجع | ||
[1] A. A. Albert, Quasigroups I, Trans. Amer. Math. Soc., 54 (1943) 507–519.
[2] R. H. Bruck, Contributions to the Theory of Loops, Trans. Amer. Math. Soc., 60 (1946) 245–354.
[3] A. Figula, The multiplication groups of 2-dimensional topological loops, ´ J. Group Theory, 12 (2009) 419–429.
[4] A. Figula, Three-dimensional topological loops with solvable multiplication groups, ´ Comm. Algebra, 42 (2014) 444– 468. [5] A. Figula and M. Lattuca, Three-dimensional topological loops with nilpotent multiplication groups, ´ J. Lie Theory, 25 (2015) 787–805. [6] A. Figula, Quasi-simple Lie groups as multiplication groups of topological loops, ´ Adv. Geom., 15 (2015) 315–331. [7] A. A. Figula, Al-Abayechi: Topological loops having solvable indecomposable Lie groups as their multiplication ´ groups, submitted to Transform. Groups, 2018. [8] K. H. Hofmann and K. Strambach, Topological and analytical loops, In: Quasigroups and Loops: Theory and Applications (Eds. O. Chein, H. O. Pflugfelder and J. D. H. Smith), 205–262, Heldermann-Verlag, Berlin, 1990.
[9] G. M. Mubarakzyanov, Classification of Solvable Lie Algebras in dimension six with one non-nilpotent basis element, Izv. Vyssh. Uchebn. Zaved. Mat., 4 (1963) 104–116. [10] P. T. Nagy and K. Strambach, Loops in Group Theory and Lie Theory de Gruyter Expositions in Mathematics, 35, Walter de Gruyter GmbH & Co. KG, Berlin, 2002. [11] M. Niemenmaa and T. Kepka, On Multiplication Groups of Loops, J. Algebra, 135 (1990) 112–122.
[12] A. Shabanskaya and G. Thompson, Six-dimensional Lie algebras with a five-dimensional nilradical, J. of Lie Theory, 23 (2013) 313–355. [13] A. Vesanen, Solvable loops and groups, J. Algebra, 180 (1996) 862–876. | ||
آمار تعداد مشاهده مقاله: 687 تعداد دریافت فایل اصل مقاله: 641 |