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Dergiler / International Electronic Journal of Algebra / 2010 / Cilt: 7 - Sayı: 7

NEW CRITERIA FOR p-NILPOTENCE OF FINITE GROUPS

Shitian LİU
Sayfa
120–127
Yayın Tarihi
2010-06-01
DOI
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In this paper, we investigate the structure of a finite group G under the assumption that certain subgroups are X-g pronormal, where X = F(G) is the Fitting subgroup of G.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:A subgroup H is X-g pronormal in G if, for H, X ≤ G and g ∈ G, H ∩ X and Hg ∩ X are conjugate in J = hH ∩ X, Hg ∩ Xi.
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Temel Bulgular & Veri:A subgroup H is X-g pronormal in G if, for H, X ≤ G and g ∈ G, H ∩ X and Hg ∩ X are conjugate in J = hH ∩ X, Hg ∩ Xi.
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Sonuç & Katkı:In this paper, we investigate the structure of a finite group G under the assumption that certain subgroups are X-g pronormal, where X = F(G) is the Fitting subgroup of G.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:F(G)-g pronormal subgroups · Sylow p-subgroup · maximal subgroups

Abstract

A subgroup H is X-g pronormal in G if, for H, X ≤ G and g ∈ G, H ∩ X and Hg ∩ X are conjugate in J = hH ∩ X, Hg ∩ Xi. In this paper, we investigate the structure of a finite group G under the assumption that certain subgroups are X-g pronormal, where X = F(G) is the Fitting subgroup of G.

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Bu Makaleye Atıf Yap

LİU, S. (2010). NEW CRITERIA FOR p-NILPOTENCE OF FINITE GROUPS. International Electronic Journal of Algebra, Cilt: 7 - Sayı: 7, 120–127. https://ajindex.com/articles/832532

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Kaynakça (11)

  1. M. Asaad, On the supersolvability of finite groups, I, Acta Math. Acad. Sci. Hungar., 38(1-4) (1981), 57-59.
  2. M. Asaad, Some results on p-nilpotence and supersolvability of fintie groups, Comm. Algebra, 34 (2006), 4217-4224.
  3. M. Asaad, On p-nilpotence and supersolvability of finite groups, Comm. Alge- bra, 34 (2006), 189-195.
  4. M. Asaad, M. Ramadan, and A. Shaalan, Influence of π-quasinormality of maximal subgroups of Sylow subgroups of Fitting subgroup of a finite group, Arch. Math., 56 (1991), 521-527.
  5. M. Bianchi, A. G. B. Mauri, M. Herzog, and L. Verard, On finite solvable groups in which normality is a transitive relation, J. Group Theory, 3 (2000), 156. P. Cs¨org¨o, and M. Herzog, On supersolvable groups and the nilpotator, Comm. Algebra, 32(2) (2004), 609-620. A. D’Anillo, Groups in which n-maximal subgroups are dualpronormal, Rend. Sem. Mat. Padova, 84 (1990), 83-90. R. Dark, and A. D. Feldman, Charcterization of injectors in finite soluble groups, J. Group Theory, 9 (2006), 775-785. K. Doerk, and T. Hawkes, Finite Soluble Groups, Walter de Gruyter, New York, 1992.
  6. D. Gorenstein, Finite Groups, 2nd, AMS Chelsea Pub., Rhode Island, 1980.
  7. H. Huppert, Endliche Gruppen I, Springer-Verlag, New York, 1967.
  8. D. Li and X. Guo, The influence of c-normality of subgroups on the structure of finite groups II, Comm. Algebra, 26 (1998), 1913-1922.
  9. D. J. Robinson, A Course in the Theory of Groups, 2nd, Springer-Verlag, New York, 1996. H. Wei, and Y. Wang, On c*-normality and its properties, J. Group Theory, (2007), 211-223.
  10. A. Yokoyama, Finite solvable groups whose F-hypercenter containing all mini- mal subgroups, Arch. Math., 26 (1975), 123-130.
  11. H. J. Zassenhaus, The Theory of Groups, 2nd, Chelsea Pub.Co., New York, Shitian Liu School of Science Sichuan University of Science & Engineering Zigong, 643000, P.R.China e-mail: [email protected]