پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 42 |
| تعداد شماره‌ها | 1,537 |
| تعداد مقالات | 12,639 |
| تعداد مشاهده مقاله | 26,036,336 |
| تعداد دریافت فایل اصل مقاله | 10,697,771 |
Subgroups of arbitrary even ordinary depth | ||
| International Journal of Group Theory | ||
| دوره 10، شماره 4، اسفند 2021، صفحه 159-166 اصل مقاله (206.9 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2020.123551.1628 | ||
| نویسندگان | ||
| Hayder Janabi* 1؛ Thomas Breuer2؛ Erzsébet Horváth1 | ||
| 1Department of Algebra, Budapest University of Technology and Economics, H-1111 Budapest, M˝ uegyetem rkp. 3–9, Hungary | ||
| 2Lehrstuhl für Algebra und Zahlentheorie, RWTH Aachen University, Pontdriesch 14-16, D-52062 Aachen, German | ||
| چکیده | ||
| We show that for each positive integer $n$, there exist a group $G$ and a subgroup $H$ such that the ordinary depth $d(H, G)$ is $2n$. This solves the open problem posed by Lars Kadison whether even ordinary depth larger than $6$ can occur. | ||
| کلیدواژه‌ها | ||
| ordinary depth of a subgroup؛ distance of characters؛ Cartesian product of graphs؛ wreath product | ||
| مراجع | ||
|
[1] R. Boltje, Susanne Danz, and Burkhard K¨ulshammer, On the depth of subgroups and group algebra extensions, J. Algebra, 335 (2011) 258–281. [2] R. Boltje ans B. K¨ulshammer, Group algebra extensions of depth one, Algebra Number Theory, 5 (2011) 63–73.
[3] R. Boltje and B. K¨ulshammer, On the depth 2 condition for group algebra and Hopf algebra extensions, J. Algebra 323 (2010) 1783–1796. [4] S. Burciu, L. Kadison and Burkhard K¨ulshammer, On subgroup depth, Int. Electron. J. Algebra, 9 (2011) 133–166, With an appendix by S. Danz and B. K¨ulshammer. [5] S. Danz, The depth of some twisted group algebra extensions, Comm. Algebra, 39 (2011) 1631–1645.
[6] T. Fritzsche, The depth of subgroups of P SL(2, q) II, J. Algebra, 381 (2013) 37–53.
[7] T. Fritzsche and B. K¨ulshammer, Carolin Reiche, The depth of Young subgroups of the symmetric groups, J. Algebra, 381 (2013) 96–109. [8] The GAP Group, GAP – Groups, Algorithms, and Programming, Version 4.9.1, 2018.
[9] F. M. Goodman, P. de la Harpe and V. F. R. Jones, Coxeter graphs and towers of algebras, Mathematical Sciences Research Institute Publications, 14, Springer-Verlag, New York, 1989. [10] A. Hernandez, L. Kadison and M. Szamotulski, Subgroup depth and twisted coefficients, Comm. Algebra, 44 (2016) 3570–3591. [11] A. Hernandez, L. Kadison and Ch. Young, Algebraic quotient modules and subgroup depth, Abh. Math. Semin. Univ. Hambg., 84 (2014) 267–283. [12] I. M. Isaacs, Character theory of finite groups, Academic Press [Harcourt Brace Jovanovich Publishers], New York, 1976. [13] E. Horv´ath, Depth of subgroups in finite groups, Talk at Groups St Andrews in Birmingham, 2017. http://www. groupsstandrews.org/2017/slides/Horvath-E.pdf. [14] L. H´ethelyi, E. Horv´ath and F. Pet´enyi, The depth of subgroups of Sz(q), Comm. Algebra, 43 (2015) 4553–4569.
[15] L. H´ethelyi, E. Horv´ath and F. Pet´enyi, The depth of the maximal subgroups of Ree groups, Comm. Algebra 47 (2019) 37–66. [16] H. A. Janabi, T. Breuer and E. Horv´ath, Construction of subgroups of ordinary depth 2n , Manuscript 2019. [17] L. Kadison, Algebra depth in tensor categories, Bull. Belg. Math. Soc., Simon Stevin 23 (2016) 721–752.
[18] L. Kadison, Open Problems (5), https://www.math.upenn.edu/{\char126\relax}lkadison/.
[19] L. Kadison and B. K¨ulshammer, Depth two, normality, and a trace ideal condition for Frobenius extensions, Comm. Algebra, 34 (2006) 3103–3122. [20] L. Kadison and D. Nikshych, Hopf algebra actions on strongly separable extensions of depth two, Adv. Math., 163 (2001) 258–286. | ||
|
آمار تعداد مشاهده مقاله: 724 تعداد دریافت فایل اصل مقاله: 919 |
||