On the number of the irreducible characters of factor groups

Document Type: Research Paper

Author

Tarbiat Moallem University

Abstract

‎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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