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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 51 Issue: 1

Solvable groups having primitive characters of degree two

Burcu Çınarcı(PİRİ REİS ÜNİVERSİTESİ)0000-0003-1202-0968
Temha Erkoç(İSTANBUL ÜNİVERSİTESİ)0000-0001-5437-3679
Sayfa
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Yayın Tarihi
2022-02-14
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Then we classify all finite solvable groups having at most five nonlinear monolithic characters one of which is primitive of degree two.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we are interested in the classification of finite solvable groups having primitive characters of degree two.
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Temel Bulgular & Veri:We first determine all finite solvable groups having both a faithful primitive character of degree two and a faithful real-valued irreducible character.
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Sonuç & Katkı:Then we classify all finite solvable groups having at most five nonlinear monolithic characters one of which is primitive of degree two.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Solvable groups · Primitive characters · Monolithic characters

Abstract

In this paper, we are interested in the classification of finite solvable groups having primitive characters of degree two. We first determine all finite solvable groups having both a faithful primitive character of degree two and a faithful real-valued irreducible character. Then we classify all finite solvable groups having at most five nonlinear monolithic characters one of which is primitive of degree two.

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Bu Makaleye Atıf Yap

Çınarcı, B., Erkoç, T. (2022). Solvable groups having primitive characters of degree two. Hacettepe Journal of Mathematics and Statistics, Volume: 51 Issue: 1. https://doi.org/10.15672/hujms.892294

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Kaynakça (8)

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  4. T. Erkoç and B. Çınarcı, Monolithic characters of real groups, Comm. Algebra 49 (8), 3192-3199, 2021.
  5. T. Erkoç and B. Çınarcı, Finite solvable groups with few imprimitive irreducible characters, J. Algebra Appl. 2020. https://doi.org/10.1142/S0219498822500669.
  6. I.M. Isaacs, Character Theory of Finite Groups, Academic Press, New York, 1976.
  7. O. Manz and T.R. Wolf, Representations of Solvable Groups, London Mathematical Society Lecture Note Series 185, Cambridge University Press, Cambridge, 1993.
  8. G.M. Seitz, Finite groups having only one irreducible representation of degree greater than one, Proc. Am. Math. Soc. 19, 459-461, 1968.