Abstract
G bir sonlu grup olsun. Bir χ indirgenemez karakterine, eğer G/ker(χ) bölüm grubunun yalnız bir tane minimal normal alt grubu varsa monolitik karakter denir. Bu çalışmada, G grubunun mertebesini bölen en küçük asal sayı q olmak üzere, G derecesi q olan bir sadık imprimitif monolitik karaktere sahipse ya bir abelyen olmayan q-grubu ya da q mertebeli Frobenius tümleyeni olan bir Frobenius grubu olduğunu ispat ediyoruz. Lineer olmayan tüm indirgenemez karakterleri monolitik olan sonlu grupları da bazı koşullar altında sınıflandırıyoruz.
Supporting Institution
TÜBİTAK
Project Number
119F295
References
- [1] Y.G. Berkovich and E.M. Zhmud, Characters of Finite Groups Part 2, American Mathemetical Society, 1999.
- [2] Y.G. Berkovich, “On Isaacs' three character degrees theorem”, Proc. Am. Math. Soc. vol. 125, no. 3, pp. 669-677, 1997 .
- [3] B. Huppert, Endliche Gruppen I, Springer, Berlin, 1967.
- [4] I.M. Isaacs, Character Theory of Finite Groups, Academic Press, New York, 1976.
- [5] I.M. Isaacs, Algebra: A Graduate Course, Brooks/Cole, Pacific Grove, CA, 1994.
- [6] O. Manz and T.R. Wolf, Representations of Solvable Groups, London Mathematical Society Lecture Note Series, vol. 185, Cambridge University Press, Cambridge, 1993.
Abstract
Let G be a finite group. An irreducible character χ is called monolithic when the factor group G/ker(χ) has unique minimal normal subgroup. In this paper, we prove that for the smallest prime q dividing the order of G if G has a faithful imprimitive monolithic character of degree q, then G becomes a nonabelian q-group or a Frobenius group with cyclic Frobenius complement whose order is q. Under certain conditions, we also classify finite groups in which their nonlinear irreducible characters are monolithic.
Project Number
119F295
References
- [1] Y.G. Berkovich and E.M. Zhmud, Characters of Finite Groups Part 2, American Mathemetical Society, 1999.
- [2] Y.G. Berkovich, “On Isaacs' three character degrees theorem”, Proc. Am. Math. Soc. vol. 125, no. 3, pp. 669-677, 1997 .
- [3] B. Huppert, Endliche Gruppen I, Springer, Berlin, 1967.
- [4] I.M. Isaacs, Character Theory of Finite Groups, Academic Press, New York, 1976.
- [5] I.M. Isaacs, Algebra: A Graduate Course, Brooks/Cole, Pacific Grove, CA, 1994.
- [6] O. Manz and T.R. Wolf, Representations of Solvable Groups, London Mathematical Society Lecture Note Series, vol. 185, Cambridge University Press, Cambridge, 1993.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Articles |
| Authors | |
| Project Number | 119F295 |
| Publication Date | July 31, 2021 |
| Published in Issue | Year 2021 Volume: 9 Issue: 4 |
