On the number of the irreducible characters of factor groups

Document Type: Research Paper


Tarbiat Moallem University


‎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.


Main Subjects

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.