پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 43 |
| تعداد شمارهها | 1,640 |
| تعداد مقالات | 13,343 |
| تعداد مشاهده مقاله | 29,979,684 |
| تعداد دریافت فایل اصل مقاله | 12,001,398 |
A probabilistic version of a theorem of László Kovács and Hyo-Seob Sim | ||
| International Journal of Group Theory | ||
| مقاله 2، دوره 9، شماره 1، خرداد 2020، صفحه 1-6 اصل مقاله (197.72 K) | ||
| نوع مقاله: Ischia Group Theory 2018 | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2018.112531.1496 | ||
| نویسندگان | ||
| Andrea Lucchini* 1؛ Mariapia Moscatiello2 | ||
| 1Dipartimento di Matematica Università di Padova | ||
| 2Dipartimento di Matematica Università di Padova | ||
| چکیده | ||
| For a finite group group, denote by $\mathcal V(G)$ the smallest positive integer $k$ with the property that the probability of generating $G$ by $k$ randomly chosen elements is at least $1/e.$ Let $G$ be a finite soluble group. {Assume} that for every $p\in \pi(G)$ there exists $G_p\leq G$ such that $p$ does not divide $|G:G_p|$ and ${\mathcal V}(G_p)\leq d.$ Then ${\mathcal V}(G)\leq d+7.$ | ||
| کلیدواژهها | ||
| Finite soluble groups؛ generation of finite groups | ||
| مراجع | ||
|
[1] A. Ballester-Bolinches and L. M. Ezquerro, Classes of finite groups, Mathematics and Its Applications (Springer), 584, Springer, Dordrecht, 2006. [2] W. Gasch¨utz, Praefrattinigruppen, Arch. Mat., 13 (1962) 418–426.
[3] W. M. Kantor and A. Lubotzky, The probability of generating a finite classical group, Geom. Ded., 36 (1990) 67–87.
[4] L. G Kov´acs and Hyo-Seob Sim, Generating finite soluble groups, Indag. Math. (N. S.), 2 (1991) 229–232.
[5] A. Lubotzky, The expected number of random elements to generate a finite group, J. Algebra, 257 (2002) 452–459.
[6] A. Lucchini, A bound on the expected number of random elements to generate a finite group all of whose Sylow subgroups are d-generated, Arch. Math. (Basel), 107 (2016) 1–8. [7] A. Lucchini, On groups with d-generator subgroups of coprime index, Comm. Algebra, 28 (2000) 1875–1880.
[8] A. Mann, Positively finitely generated groups, Forum Math., 8 (1996) 429–459. | ||
|
آمار تعداد مشاهده مقاله: 466 تعداد دریافت فایل اصل مقاله: 274 |
||