Asal Dereceli Monolitik Karakterlere Sahip Sonlu Gruplar

Year 2021, , 997 - 1001, 31.07.2021

Temha Erkoç , Burcu Çınarcı

https://doi.org/10.29130/dubited.891767

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.

Keywords

Finite Groups, Monolithic Characters, Primitive Characters

Supporting Institution

TÜBİTAK

Project Number

119F295

Finite Groups Having Monolithic Characters of Prime Degree

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.

Keywords

Finite groups, Monolithic characters, Primitive characters

Project Number

119F295

References

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