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On the number of the irreducible characters of factor groups | ||
| International Journal of Group Theory | ||
| مقاله 3، دوره 2، شماره 2، شهریور 2013، صفحه 19-24 اصل مقاله (388.25 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2013.1825 | ||
| نویسنده | ||
| Amin Saeidi* | ||
| Tarbiat Moallem University | ||
| چکیده | ||
| Let $G$ be a finite group and let $N$ be a normal subgroup of $G$. Suppose that ${\rm{Irr}} (G | N)$ is the set of the irreducible characters of $G$ that contain $N$ in their kernels. In this paper, we classify solvable groups $G$ in which the set $\mathcal{C} (G) = \{{\rm{Irr}} (G | N) | 1 \ne N \trianglelefteq G \}$ has at most three elements. We also compute the set $\mathcal{C}(G)$ for such groups. | ||
| کلیدواژه‌ها | ||
| Irreducible characters؛ Conjugacy classes؛ minimal normal subgroups؛ Frobenius groups | ||
| مراجع | ||
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M. Aschbacher (1986) Finite Group Theory Cambridge University Press, Cambridge
GAP groups Algorithms, and Programming Version 4.4.10, 2007.
I. M. Isaacs (1994) Character Theory of Finite Groups Dover, New York
A. Saeidi and S. Zandi (2012) The number of conjugacy classes contained in normal subgroups of solvable groups to appear in Journal of Algebra and its Applications
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