اخبار و اعلانات

 آمار

تعداد نشریات43
تعداد شماره‌ها1,791
تعداد مقالات14,610
تعداد مشاهده مقاله38,728,142
تعداد دریافت فایل اصل مقاله15,076,555
Dixon, Martyn, Kurdachenko, Leonid, Subbotin, Igor. (1402). Generalized nilpotent braces and nilpotent groups. , 14(1), 25-45. doi: 10.22108/ijgt.2023.138490.1860
Martyn Dixon; Leonid A. Kurdachenko; Igor Ya. Subbotin. "Generalized nilpotent braces and nilpotent groups". , 14, 1, 1402, 25-45. doi: 10.22108/ijgt.2023.138490.1860
Dixon, Martyn, Kurdachenko, Leonid, Subbotin, Igor. (1402). 'Generalized nilpotent braces and nilpotent groups', , 14(1), pp. 25-45. doi: 10.22108/ijgt.2023.138490.1860
Dixon, Martyn, Kurdachenko, Leonid, Subbotin, Igor. Generalized nilpotent braces and nilpotent groups. , 1402; 14(1): 25-45. doi: 10.22108/ijgt.2023.138490.1860

Generalized nilpotent braces and nilpotent groups

International Journal of Group Theory
مقاله 5، دوره 14، شماره 1، خرداد 2025، صفحه 25-45    اصل مقاله (476.96 K)
نوع مقاله: Ischia Group Theory 2022
شناسه دیجیتال (DOI): 10.22108/ijgt.2023.138490.1860
نویسندگان
Martyn Dixon* 1؛ Leonid A. Kurdachenko2؛ Igor Ya. Subbotin3
1Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, U. S. A.
2Department of Algebra, Facultet of mathematic and mechanik, National University of Dnepropetrovsk, Gagarin prospect 72, Dnipro 10 49010, Ukraine
3Department of Mathematics and Natural Sciences, National University,5245 Pacific Concourse Drive, Los Angeles, CA 90045-6904, U. S. A.
چکیده
The authors give a brief survey of some results concerning nilpotent braces and their generalizations. Various results concerning $\star$-hypercentral and locally $\star$-nilpotent braces are given.
کلیدواژه‌ها
Brace؛ nilpotent brace؛ $\star$-hypercentral brace؛ locally $\star$-nilpotent brace
مراجع

[1] D. Bachiller, Classification of braces of order p3 , J. Pure Appl. Algebra, 219 (2015) no. 8 3568–3603.
[2] M. Bonatto and P. Jedlička, Central nilpotency of skew braces, J. Algebra Appl., 22 (2023) no. 12 Paper No. 2350255.
[3] F. Cedó, Left braces: solutions of the Yang-Baxter equation, Adv. Group Theory Appl., 5 (2018) 33–90.
[4] F. Cedó, T. Gateva-Ivanova and A. Smoktunowicz, On the Yang-Baxter equation and left nilpotent left braces, J. Pure Appl. Algebra, 221 (2017) no. 4 751–756.
[5] F. Cedó, A. Smoktunowicz and L. Vendramin, Skew left braces of nilpotent type, Proc. Lond. Math. Soc. (3), 118 (2019) no. 6 1367–1392.
[6] S. N. Chernikov, On special p-groups, Mat. Sbornik N. S., 27 no. 69 (1950) 185–200.
[7] I. Colazzo, M. Ferrara and M. Trombetti, On derived-indecomposable solutions of the Yang-Baxter equation, ArXiv Math: 2210.08598.
[8] P. Hall, The Frattini subgroups of finitely generated groups, Proc. London Math. Soc. (3), 11 (1961) 327–352.
[9] E. Jespers, A. van Antwerpen and L. Vendramin, Nilpotency of skew braces and multipermutation solutions of the Yang-Baxter equation, Commun. Contemp. Math., 25 20 pp.

[10] W. Rump, A decomposition theorem for square-free unitary solutions of the quantum Yang-Baxter equation, Adv. Math., 193 (2005) no. 1 40–55.
[11] W. Rump,, Braces, radical rings, and the quantum Yang-Baxter equation, J. Algebra, 307 (2007) no. 1 153–[11]
170.
[12] A. Smoktunowicz, On Engel groups, nilpotent groups, rings, braces and the Yang-Baxter equation, Trans. Amer. Math. Soc., 370 (2018) no. 9 6535–6564.
[13] A. Smoktunowicz, Algebraic approach to Rump’s results on relations between braces and pre-Lie algebras, J. Algebra Appl., 21 (2022) no. 3 13 pp.
[14] M. Trombetti, The structure skew brace associated with a finite non-degenerate solution of the yang-baxter equation is finitely presented, to appear Proc. American Math. Soc., (2023) 11 pp.

آمار
تعداد مشاهده مقاله: 251
تعداد دریافت فایل اصل مقاله: 311


سامانه مدیریت نشریات علمی. طراحی و پیاده سازی از سیناوب