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On Hall subgroups of a finite group

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Central European Journal of Mathematics

Abstract

New criteria of existence and conjugacy of Hall subgroups of finite groups are given.

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References

  1. Ballester-Bolinches A., Esteban-Romero R., Asaad M., Products of Finite Groups, de Gruyter Exp. Math., 53, Walter de Gruyter, Berlin, 2010

    Book  MATH  Google Scholar 

  2. Čunihin S.A., On π-separate groups, Doklady Akad. Nauk SSSR (N.S.), 1948, 59, 443–445 (in Russian)

    MathSciNet  Google Scholar 

  3. Čunihin S.A., On weakening the conditions in theorems of Sylow type, Doklady Akad. Nauk SSSR (N.S.), 1952, 83, 663–665 (in Russian)

    MathSciNet  Google Scholar 

  4. Čunihin S.A., On existence and conjugateness of subgroups of a finite group, Mat. Sb. (N.S.), 1953, 33(75), 111–132 (in Russian)

    Google Scholar 

  5. Doerk K., Hawkes T., Finite Soluble Groups, de Gruyter Exp. Math., 4, Walter de Gruyter, Berlin, 1992

    Book  Google Scholar 

  6. Foguel N., On seminormal subgroups, J. Algebra, 1994, 165(3), 633–635

    Article  MathSciNet  MATH  Google Scholar 

  7. Guo W., Shum K.P., Skiba A.N., X-semipermutable subgroups of finite groups, J. Algebra, 2007, 315(1), 31–41

    Article  MathSciNet  MATH  Google Scholar 

  8. Guo W.B., Skiba A.N., Criteria of existence of Hall subgroups in non-soluble finite groups, Acta Math. Sin. (Engl. Ser.), 2010, 26(2), 295–304

    Article  MathSciNet  MATH  Google Scholar 

  9. Guo W., Skiba A.N., New criterions of existence and conjugacy of Hall subgroups of finite groups, Proc. Amer. Math. Soc., 2011, 139(7), 2327–2336

    Article  MathSciNet  MATH  Google Scholar 

  10. Hall P., A characteristic property of soluble groups, J. London Math. Soc., 1937, s1–12(3), 198–200

    Article  Google Scholar 

  11. Hall P., Theorems like Sylow’s, Proc. London Math. Soc., 1956, 6, 286–304

    Article  MathSciNet  MATH  Google Scholar 

  12. Kegel O.H., Produkte nilpotenter Gruppen, Arch. Math. (Basel), 1961, 12, 90–93

    Article  MathSciNet  MATH  Google Scholar 

  13. Kegel O.H, Sylow-Gruppen and Subnormalteiler endlicher Gruppen, Math. Z., 1962, 78, 205–221

    Article  MathSciNet  MATH  Google Scholar 

  14. Knyagina V.N., Monakhov V.S., On the π′-properties of a finite group possessing a Hall π-subgroup, Sib. Math. J., 2011, 52(2), 234–243

    Article  MathSciNet  MATH  Google Scholar 

  15. Revin D.O., Vdovin E.P., Hall subgroups of finite groups, In: Ischia Group Theory 2004, Naples, March 31–April 3, 2004 Contemp. Math., 402, American Mathematical Society/Bar-Ilan University, Providence/Ramat Gan, 2006, 229–265

    Google Scholar 

  16. Rusakov S.A., Analogues of Sylow’s theorem on the existence and imbedding of subgroups, Sibirsk. Mat. Zh., 1963, 4(2), 325–342 (in Russian)

    MathSciNet  MATH  Google Scholar 

  17. Shemetkov L.A., On Sylow properties of finite groups, Dokl. Akad. Nauk BSSR, 1972, 16(10), 881–883 (in Russian)

    MathSciNet  MATH  Google Scholar 

  18. Shemetkov L.A., Formations of Finite Groups, Nauka, Moscow, 1978 (in Russian)

    MATH  Google Scholar 

  19. Vdovin E.P., Revin D.O., A conjugacy criterion for Hall subgroups in finite groups, Sib. Math. J., 2010, 51(3), 402–409

    Article  MathSciNet  MATH  Google Scholar 

  20. Wielandt H., Zum Satz von Sylow. II, Math. Z., 1959, 71, 461–462

    Article  MathSciNet  MATH  Google Scholar 

  21. Wielandt H., Subnormal Subgroups and Permutation Groups, Ohio State University, Columbus, 1971

    Google Scholar 

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Correspondence to Alexander N. Skiba.

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Guo, W., Skiba, A.N. On Hall subgroups of a finite group. centr.eur.j.math. 11, 1177–1187 (2013). https://doi.org/10.2478/s11533-013-0239-3

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  • DOI: https://doi.org/10.2478/s11533-013-0239-3

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