Abstract
Supporting Institution
TÜBİTAK
Project Number
119F295
References
- [1] Isaacs I. M., Character Theory of Finite Groups, Academic Press, New York, (1976.
- [2] Seitz G.M., Finite groups having only one irreducible representation of degree greater than one. Proc. Am. Math. Soc., (19) (1968) 459-461.
- [3] Manz O., Wolf T.R., Representations of Solvable Groups, London Mathematical Society Lecture Note Series, (185), Cambridge University Press, Cambridge (1993).
- [4] Berkovich Y., Zhmud E. M., Characters of Finite Groups. Part 2, American Mathemetical Society, (1999).
- [5] Berkovich Y., On Isaacs’ three character degrees theorem, Proc. Am. Math. Soc. 125 (3) (1997) 669-677.
Abstract
Let G be a finite group and χ∈Irr(G), where Irr(G) denotes the set of all irreducible characters of G. The kernel of χ is defined by ker(χ)={ g∈G ┤| χ(g)=χ(1)}, where χ(1) is the character degree of χ. The irreducible character χ of G is called as monolithic when the factor group G/ker(χ) has only one minimal normal subgroup. In this study, we have proven some results by concentrating on the kernels of nonlinear irreducible characters of G. First, we have provided an alternative proof for the classification of finite groups possessing two nonlinear irreducible characters by using their kernels. Also, we have presented the structure the solvable group G in which every nonlinear monolithic characters has same kernel
Project Number
119F295
References
- [1] Isaacs I. M., Character Theory of Finite Groups, Academic Press, New York, (1976.
- [2] Seitz G.M., Finite groups having only one irreducible representation of degree greater than one. Proc. Am. Math. Soc., (19) (1968) 459-461.
- [3] Manz O., Wolf T.R., Representations of Solvable Groups, London Mathematical Society Lecture Note Series, (185), Cambridge University Press, Cambridge (1993).
- [4] Berkovich Y., Zhmud E. M., Characters of Finite Groups. Part 2, American Mathemetical Society, (1999).
- [5] Berkovich Y., On Isaacs’ three character degrees theorem, Proc. Am. Math. Soc. 125 (3) (1997) 669-677.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Natural Sciences |
| Authors | |
| Project Number | 119F295 |
| Publication Date | September 30, 2022 |
| Submission Date | March 29, 2021 |
| Acceptance Date | May 6, 2022 |
| Published in Issue | Year 2022 |