On the number of the irreducible characters of factor groups
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 triangl...
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| Format: | Article |
| Language: | English |
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University of Isfahan
2013-06-01
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| Series: | International Journal of Group Theory |
| Subjects: | |
| Online Access: | http://www.theoryofgroups.ir/?_action=showPDF&article=1825&_ob=6001fd72971d120567ffe1fb9aabb3b8&fileName=full_text.pdf |
| Summary: | 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. |
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| ISSN: | 2251-7650 2251-7669 |