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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 1

A note on the embedding properties of p-subgroups in finite groups

Xiuyun GUO
Boru Zhang
Sayfa
102–111
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In this note, we prove that a finite group G is p-supersolvable if and only if there exists a power d of p with p2 ≤ d d if there exists a power d of p with 1 ≤ d < |P| such that H ∩Op(G∗ p2) is normal in Op(G) for all non-meta-cyclic normal subgroups H of P with |H|= d.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this note, we prove that a finite group G is p-supersolvable if and only if there exists a power d of p with p2 ≤ d d if there exists a power d of p with 1 ≤ d < |P| such that H ∩Op(G∗ p2) is normal in Op(G) for all non-meta-cyclic normal subgroups H of P with |H|= d.
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Temel Bulgular & Veri:In this note, we prove that a finite group G is p-supersolvable if and only if there exists a power d of p with p2 ≤ d d if there exists a power d of p with 1 ≤ d < |P| such that H ∩Op(G∗ p2) is normal in Op(G) for all non-meta-cyclic normal subgroups H of P with |H|= d.
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Sonuç & Katkı:In this note, we prove that a finite group G is p-supersolvable if and only if there exists a power d of p with p2 ≤ d d if there exists a power d of p with 1 ≤ d < |P| such that H ∩Op(G∗ p2) is normal in Op(G) for all non-meta-cyclic normal subgroups H of P with |H|= d.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this note, we prove that a finite group G is p-supersolvable if and only if there exists a power d of p with p2 ≤ d d if there exists a power d of p with 1 ≤ d < |P| such that H ∩Op(G∗ p2) is normal in Op(G) for all non-meta-cyclic normal subgroups H of P with |H|= d.

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Bu Makaleye Atıf Yap

GUO, X., Zhang, B. (2022). A note on the embedding properties of p-subgroups in finite groups. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 1, 102–111. https://ajindex.com/articles/529754

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Kaynakça (12)

  1. A. Ballester-Bolinches, R. Esteban-Romero and S. Qiao, A note on a result of Guo and Isaacs about p-supersolubility of finite groups, Arch. Math. (Basel) 106 (6), 501-506, 2016. Y. Berkovich and I.M. Isaacs, p-Supersolvability and actions on p-groups stabilizing certain subgroups, J. Algebra 414 82-94, 2014.
  2. Y. Berkovich and Z. Janko, Groups of prime power order Vol. 1, Walter de Gruyter, Berlin, New York, 2008.
  3. Y. Berkovich and Z. Janko, Groups of prime power order Vol 2, Walter de Gruyter, Berlin, New York, 2008.
  4. K. Doerk and T. Hawkes, Finite soluble groups, Walter de Gruyter, Berlin, 1992.
  5. Y. Guo and I.M. Isaacs, Conditions on p-subgroups implying p-nilpotence or p-supersolvability, Arch. Math. (Basel) 105 (3), 215-222, 2015.
  6. X. Guo and H. Meng, Actions on p-groups with the kernel containing the -residuals, Comm. Algebra, 45 (7), 3022-3033, 2017.
  7. X. Guo and B. Zhang, Conditions on p-subgroups implying p-supersolvability, J. Al-gebra Appl. 16 (10) 1750196, 9 pages, 2017.
  8. B. Huppert, Endliche Gruppen I, Springer-Verlag, Berlin, 1967.
  9. I.M. Isaacs, Finite group theory, Graduate Studies in Math. 92 AMS Providence, 2008.
  10. R.M. Peacock, Groups with a cyclic sylow subgroup, J. Algebra 56, 506-509, 1979.
  11. L. Wang and Y. Wang, On s-semipermutable maximal and minimal subgroups of Sylow p-subgroups of finite groups, Comm. Algebra 34, 143-149, 2006.
  12. H. Yu, Some su cient and necessary conditions for p-supersolvablity and p-nilpotence of a finite group. J. Algebra Appl. 16 (2), 1750052, 9 pages, 2017.