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On weakly SΦ-supplemented subgroups of finite groups

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Abstract

Let G be a finite group. We say that a subgroup H of G is weakly SΦ-supplemented in G if G has a subgroup T such that G = HT and H∩T ≤ Φ(H)H sG , where H sG is the subgroup of H generated by all those subgroups of H that are s-permutable in G. In this paper, we investigate the influence of weakly SΦ-supplemented subgroups on the structure of finite groups. Some new characterizations of p-nilpotency and supersolubility of finite groups are obtained.

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References

  1. Ballester-Bolinches A., Wang Y., and Guo X., “c-Supplemented subgroups of finite groups,” Glasgow Math. J., 42, 383–389 (2000).

    Article  MathSciNet  MATH  Google Scholar 

  2. Guo W., Xie F., and Li B., “Some open questions in the theory of generalized permutable subgroups,” Sci. China, Ser. A, 52, No. 10, 2132–2144 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  3. Skiba A. N., “On weakly s-permutable subgroups of finite groups,” J. Algebra, 315, 192–209 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  4. Li J. and Xie F., “On inequalities of subgroups and the structure of finite groups,” J. Ineq. Appl., 1, 427 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  5. Doerk K. and Hawkes T., Finite Soluble Groups, Walter de Gruyter, Berlin; New York (1992).

    Book  MATH  Google Scholar 

  6. Gorenstein D., Finite Groups, Chelsea Publ. Comp., New York (1980).

    MATH  Google Scholar 

  7. Guo W., The Theory of Classes of Groups, Sci. Press-Kluwer Acad. Publ., Beijing; New York; Dordrecht; Boston; London (2000).

    Google Scholar 

  8. Guo W., Structure Theory for Canonical Classes of Finite Groups, Springer-Verlag, Berlin; Heidelberg (2015).

    Book  MATH  Google Scholar 

  9. Kegel O., “Sylow-Gruppen and Subnormalteiler endlicher Gruppen,” Math. Z., 78, 205–221 (1962).

    Article  MathSciNet  MATH  Google Scholar 

  10. Schmid P., “Subgroup permutable with all Sylow subgroups,” J. Algebra, 207, 285–293 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  11. Guo W. and Skiba A. N., “Finite groups with generalized Ore supplement conditions for primary subgroups,” J. Algebra, 432, 205–227 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  12. Guo W., Skiba A. N., and Tang X., “On boundary factors and traces of subgroups of finite groups,” Comm. Math. Stat., 2, 349–361 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  13. Skiba A. N., “On two questions of L. A. Shemetkov concerning hypercyclically embedded subgroups of finite groups,” J. Group Theory, 13, 841–850 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  14. Huppert B. and Blackburn N., Finite Groups. III, Springer-Verlag, Berlin; New York (1982).

    MATH  Google Scholar 

  15. Guo W. and Skiba A. N., “On FF * -hypercentral subgroups of finite groups,” J. Algebra, 372, 275–292 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  16. Chen X., Guo W., and Skiba A. N., “Some conditions under which a finite group belongs to a Baer-local formation,” Comm. Algebra, 42, 4188–4203 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  17. Chen X. and Guo W., “On o-supplemented subgroups of a finite group,” Comm. Algebra, 44, 731–745 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  18. Wang Y., Wei H., and Li Y., “A generalization of a theorem of Kramer and its applications,” Bull. Austral. Math. Soc., 65, 467–475 (2002).

    Article  MathSciNet  Google Scholar 

  19. Guo W. and Skiba A. N., “On the intersection of the F-maximal subgroups and the generalized F-hypercentre of a finite groups,” J. Algebra, 366, 112–125 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  20. Huppert B., Endliche Gruppen. I, Springer-Verlag, Berlin; Heidelberg; New York (1967).

    Book  MATH  Google Scholar 

  21. Robinson D. J. S., A Course in the Theory of Groups, Springer-Verlag, New York (1982).

    Book  MATH  Google Scholar 

  22. Li Y. and Li B., “On minimal weakly s-supplemented subgroups of finite groups,” J. Algebra Appl., 10, 811–820 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  23. Huppert B., “Normalteiler und maximale Untergruppen endlicher Gruppen,” Math. Z., 60, 409–434 (1954).

    Article  MathSciNet  MATH  Google Scholar 

  24. Ballester-Bolinches A. and Esteban-Romero R., “On minimal non-supersoluble groups,” Rev. Mat. Iberoam., 23, No. 1, 127–142 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  25. Semenchuk V. N., “Minimal non-F-groups,” Algebra and Logic, 18, No. 3, 349–382 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  26. Wei H., Wang Y., and Li Y., “On c-supplemented maximal and minimal subgroups of Sylow subgroups of finite groups,” Proc. Amer. Math. Soc., 132, 2197–2204 (2004).

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, P. R. China

    Zh. Wu, Y. Mao & W. Guo

  2. School of Mathematics and Computer, University of Datong of Shanxi, Datong, P. R. China

    Y. Mao

Authors
  1. Zh. Wu
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  2. Y. Mao
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  3. W. Guo
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Correspondence to W. Guo.

Additional information

Original Russian Text Copyright © 2016 Wu Zh., Mao Y., and Guo W.

The authors were supported by the NNSF of China (Grant 11371335) and the Wu Wen-Tsun Key Laboratory of Mathematics of the Chinese Academy of Sciences.

Hefei; Datong. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 57, No. 4, pp. 889–898, July–August, 2016; DOI: 10.17377/smzh.2016.57.411. Original article submitted June 1, 2015.

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Wu, Z., Mao, Y. & Guo, W. On weakly SΦ-supplemented subgroups of finite groups. Sib Math J 57, 696–703 (2016). https://doi.org/10.1134/S003744661604011X

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  • DOI: https://doi.org/10.1134/S003744661604011X

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