On a class of generalised Schmidt groups

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• 作者：A. Ballester-Bolinches (1)
  R. Esteban-Romero (1) (2)
  Qinhui Jiang (3) (4)
  Xianhua Li (5)
  
  1. Departament d鈥櫭€lgebra ; Universitat de Val猫ncia ; Dr. Moliner ; 50 ; 46100 ; Burjassot ; Val猫ncia ; Spain
  2. Institut Universitari de Matem脿tica Pura i Aplicada ; Universitat Polit猫cnica de Val猫ncia ; Cam铆 de Vera ; s/n ; 46022 ; Val猫ncia ; Spain
  3. School of Mathematical Sciences ; University of Jinan ; Jinan ; 250002 ; China
  4. Department of Mathematics ; Shanghai University ; Shanghai ; 200444 ; China
  5. School of Mathematical Science ; Soochow University ; Suzhou ; 215006 ; China
  
• 关键词：Finite groups ; Nilpotent groups ; Maximal subgroups ; 20D05 ; 20D10 ; 20F16
• 刊名：Annali di Matematica Pura ed Applicata
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：194
• 期：1
• 页码：77-86
• 全文大小：168 KB
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  3. Ballester-Bolinches, A., Cossey, J., Esteban-Romero, R.: On the abnormal structure of finite groups. Rev. Math. Iberoam. (in press)
  4. Ballester-Bolinches, A., Ezquerro, L.M.: Classes of finite groups. In: Hazewinkel, M. (ed.) Mathematics and its Applications, vol. 584. Springer, New York (2006)
  5. Beidleman, J.C., Heineken, H.: Minimal non- \({\cal F}\) -groups. Ric. Mat. 58(1), 33鈥?1 (2009) get="_blank" title="It opens in new window">CrossRef
  6. Conway, J.H., Curtis, R.T., Norton, S.P., Parker, R.A., Wilson, R.A.: Atlas of Finite Groups. Oxford University Press, London (1985)
  7. Huppert, B.: Endliche Gruppen I. In: Eckmann, B., van der Waerden, B.L. (eds.) Die Grundlehren der Mathematischen Wissenschaften, vol. 134, Springer, Berlin (1967)
  8. Huppert, B., Blackburn, N.: Finite groups III. In: Eckmann, B., Varadhan, S.R.S. (eds.) Die Grundlehren der Mathematischen Wissenschaften, vol. 243, Springer, Berlin (1982)
  9. Huppert, B., Lempken, W.: Simple groups of order divisible by at most four primes. Izv. Gomel. Gos. Univ. Im. F. Skoriny 3, 64鈥?5 (2000)
  10. Li, C.H., Zhang, H.: The finite primitive groups with soluble stabilizers, and the edge-primitive \(s\) -arc transitive graphs. Proc. Lond. Math. Soc. 103(3), 441鈥?72 (2011) get="_blank" title="It opens in new window">CrossRef
  11. Li, Q., Guo, X.: On generalization of minimal non-nilpotent groups. Lobachevskii J. Math. 31(3), 239鈥?43 (2010) get="_blank" title="It opens in new window">CrossRef
  12. Li, Q., Guo, X.: On \(p\) -nilpotence and solubility of groups. Arch. Math. (Basel) 96, 1鈥? (2011)
  13. Lukyanenko, V.O., Netbay, O.V., Skiba, A.N.: Finite groups in which every non-abnormal subgroup is \(X_s\) -permutable. Vets墨 Nats. Akad. Navuk Belarus墨 Ser. Fiz. Mat. Navuk, (4), 25鈥?9 (2009) (Russian). http://nasb.gov.by/rus/publications/vestifm/vfm09_4.php
  14. Rose, J.S.: The influence on a finite group of its proper abnormal structure. J. Lond. Math. Soc. 40, 348鈥?61 (1965) get="_blank" title="It opens in new window">CrossRef
  15. Schmidt, O.J.: 脺ber Gruppen, deren s盲mtliche Teiler spezielle Gruppen sind. Mat. Sb. 31, 366鈥?72 (1924)
  16. Skiba, A.N.: On the intersection of all maximal \(\mathfrak{F}\) -subgroups of a finite group. J. Algebra 343, 173鈥?82 (2011) gebra.2011.06.028" target="_blank" title="It opens in new window">CrossRef
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1618-1891

文摘

In this paper families of non-nilpotent subgroups covering the non-nilpotent part of a finite group are considered. An \(A_5\) -free group possessing one of these families is soluble, and soluble groups with this property have Fitting length at most three. A bound on the number of primes dividing the order of the group is also obtained.