EN
A Study On the Kernels of Irreducible Characters of Finite Groups
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
Keywords
Supporting Institution
TÜBİTAK
Project Number
119F295
References
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- [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
Research Article
Publication Date
September 30, 2022
Submission Date
March 29, 2021
Acceptance Date
May 6, 2022
Published in Issue
Year 2022 Volume: 43 Number: 3