پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 43 |
| تعداد شمارهها | 1,829 |
| تعداد مقالات | 14,867 |
| تعداد مشاهده مقاله | 40,782,226 |
| تعداد دریافت فایل اصل مقاله | 15,823,424 |
Character expansiveness in finite groups | ||
| International Journal of Group Theory | ||
| مقاله 2، دوره 2، شماره 2، شهریور 2013، صفحه 9-17 اصل مقاله (424.23 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2013.1660 | ||
| نویسندگان | ||
| Zoltan Halasi1؛ Attila Maroti* 2؛ Franciska Petenyi3 | ||
| 1University of Debrecen | ||
| 2Renyi Institute of Mathematics | ||
| 3Technical University of Budapest | ||
| چکیده | ||
| We say that a finite group $G$ is conjugacy expansive if for any normal subset $S$ and any conjugacy class $C$ of $G$ the normal set $SC$ consists of at least as many conjugacy classes of $G$ as $S$ does. Halasi, Mar'oti, Sidki, Bezerra have shown that a group is conjugacy expansive if and only if it is a direct product of conjugacy expansive simple or abelian groups. By considering a character analogue of the above, we say that a finite group $G$ is character expansive if for any complex character $\alpha$ and irreducible character $\chi$ of $G$ the character $\alpha \chi$ has at least as many irreducible constituents, counting without multiplicity, as $\alpha$ does. In this paper we take some initial steps in determining character expansive groups. | ||
| کلیدواژهها | ||
| Finite group؛ Irreducible characters؛ product of characters | ||
| مراجع | ||
|
C. Bessenrodt and A. Kleshchev (1999) On Kronecker products of complex
representations of the symmetric and alternating groups, Pacific J. Math. 190 (2), 201-223
W. Feit and G. M. Seitz (1989) On finite rational groups and related
topics llinois J. Math. 33 (1), 103-131
P. Erd\H os (1942) On an elementary proof of some asymptotic formulas in the theory of partitions Ann. of Math. (2) 43 (3), 437-450
P. X. Gallagher (1970) The number of conjugacy classes in a finite group Math. Z. 118, 175-179
The GAP Group (2007) GAP -- Groups, Algorithms, and Programming Version 4.4.10
C. K\"ohler and H. Pahlings (1999) Regular orbits and the $k(GV)$-problem Groups and computation III., Proceedings of the international
conference at the Ohio State University, Columbus, OH, USA, June , 15-19
W. Feit (1993) in ``Linear Algebraic
Groups and Their Representations Los Angeles, 1992", Contemp.
Math. 153, 1-9
Z. Halasi, A. Mar\'oti, S. Sidki and M. Bezerra Conjugacy expansiveness in finite groups to appear in J. Group Theory
H. W. Kuhn (1955) The Hungarian method for the assignment problem Naval Res. Logist. Quart. 2, 83-97
I. G. Macdonald (1981) Numbers of conjugacy classes in some finite
classical groups Bull. Austral. Math. Soc. 23, 23-48
\href http://www.wolfram.com/mathematica http://www.wolfram.com/mathematica
H. Nagao (1962) On a conjecture of Brauer for $p$-solvable groups J. Math. Osaka City Univ. 13, 35-38
P. Schmid (2007) The solution of the $k(GV)$ problem. ICP Advanced Texts in Mathematics 4. Imperial College Press, London
\'A. Seress (1997) Primitive groups with no regular orbits on the set of subsets Bull. London Math. Soc. 29 (6), 697-704
| ||
|
آمار تعداد مشاهده مقاله: 8,068 تعداد دریافت فایل اصل مقاله: 3,196 |
||