Öz
Destekleyen Kurum
TÜBİTAK
Proje Numarası
119F295
Kaynakça
- [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.
Öz
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
Anahtar Kelimeler
Finite groups Monolithic characters Character degrees Kernels of irreducible characters.
Proje Numarası
119F295
Kaynakça
- [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.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Natural Sciences |
| Yazarlar | |
| Proje Numarası | 119F295 |
| Yayımlanma Tarihi | 30 Eylül 2022 |
| Gönderilme Tarihi | 29 Mart 2021 |
| Kabul Tarihi | 6 Mayıs 2022 |
| Yayımlandığı Sayı | Yıl 2022 |