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Dergiler / International Electronic Journal of Algebra / 2023 / Cilt: 34 Sayı: 34

A note on the solvability of a finite group in which every non-nilpotent maximal subgroup is normal

Wenjing LIU
Jiangtao SHI
Yunfeng TIAN
Sayfa
207–209
Yayın Tarihi
2023-07-10
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We provide a new and simple proof to show that a finite group in which every non-nilpotent maximal subgroup is normal is solvable.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:We provide a new and simple proof to show that a finite group in which every non-nilpotent maximal subgroup is normal is solvable.
📊
Temel Bulgular & Veri:We provide a new and simple proof to show that a finite group in which every non-nilpotent maximal subgroup is normal is solvable.
💡
Sonuç & Katkı:We provide a new and simple proof to show that a finite group in which every non-nilpotent maximal subgroup is normal is solvable.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Non-nilpotent maximal subgroup · solvable group · normal subgroup of prime-power order

Abstract

We provide a new and simple proof to show that a finite group in which every non-nilpotent maximal subgroup is normal is solvable.

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Bu Makaleye Atıf Yap

LIU, W., SHI, J., TIAN, Y. (2023). A note on the solvability of a finite group in which every non-nilpotent maximal subgroup is normal. International Electronic Journal of Algebra, Cilt: 34 Sayı: 34, 207–209. https://ajindex.com/articles/953325

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Kaynakça (3)

  1. N. Li and J. Shi, A note on a finite group with all non-nilpotent maximal subgroups being normal, Ital. J. Pure Appl. Math., 42 (2019), 700-702.
  2. D. J. S. Robinson, A Course in the Theory of Groups (Second Edition), Springer-Verlag, New York, 1996.
  3. J. Shi, A finite group in which all non-nilpotent maximal subgroups are normal has a Sylow tower, Hokkaido Math. J., 48(2) (2019), 309-312.