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Normalizers of Sylow Subgroups in Finite Linear and Unitary Groups

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We specify normalizers of Sylow r-subgroups in finite simple linear and unitary groups for the case where r is an odd prime distinct from the characteristic of a definition field of a group.

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  • 28 July 2020

    The name of the author should read not A. V. Vasil���ev, but A. S. Vasil���ev.

References

  1. L. Kaloujnine, “La structure des p-groupes de Sylow des groupes symétriques finis,” Ann. Sci. Éc. Norm. Supér., III. Sér., 65, No. 3, 239-276 (1948).

  2. C. Chevalley, “Sur certains groupes simples,” Tôhoku Math. J., II. Ser., 7, 14-66 (1955).

  3. A. J. Weir, “Sylow p-subgroups of the classical groups over finite fields with characteristic prime to p,” Proc. Am. Math. Soc., 6, No. 4, 529-533 (1955).

    MathSciNet  MATH  Google Scholar 

  4. R. W. Carter and P. Fong, “The Sylow 2-subgroups of the finite classical groups,” J. Alg., 1, No. 1, 139-151 (1964).

  5. R. W. Carter, Simple Groups of Lie Type (Reprint of the 1972 orig.), Wiley Classics Library, Wiley, New York (1989).

  6. J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, Atlas of Finite Groups, Clarendon Press, Oxford (1985).

    MATH  Google Scholar 

  7. A. S. Kondratiev, “Normalizers of Sylow 2-subgroups in finite simple groups,” Mat. Zametki, 78, No. 3, 368-376 (2005).

    Article  MathSciNet  Google Scholar 

  8. B. Huppert and N. Blackburn, Finite Groups. III, Grundlehren Math. Wiss., 243, Springer- Verlag, Berlin (1982).

  9. R. M. Guralnick, G. Malle, and G. Navarro, “Self-normalizing Sylow subgroups,” Proc. Am. Math. Soc., 132, No. 4, 973-979 (2004).

    Article  MathSciNet  Google Scholar 

  10. E. P. Vdovin, “The structure of groups possessing Carter subgroups of odd order,” Algebra and Logic, 54, No. 2, 105-107 (2015).

  11. A. A. Volochkov, “Normalizers of Sylow subgroups in general and special linear groups over finite fields,” Vest. Perm Univ., Mat., Mekh., Inf., 20, No. 4, 14-22 (2008).

  12. P. Kleidman and M. Liebeck, The Subgroup Structure of the Finite Classical Groups, London Math. Soc. Lect. Note Ser., 129, Cambridge Univ., Cambridge (1990).

  13. J. L. Alperin and P. Fong, “Weights for symmetric and general linear groups,” J. Alg., 131, No. 1, 2-22 (1990).

    Article  MathSciNet  Google Scholar 

  14. Jianbei An, “Weights for classical groups,” Trans. Am. Math. Soc., 342, No. 1, 1-42 (1994).

    Article  MathSciNet  Google Scholar 

  15. I. M. Isaacs, Finite Group Theory, Grad. Stud. Math., 92, Am. Math. Soc., Providence, RI (2008).

  16. R. L. Griess, Jr., “Automorphisms of extra special groups and nonvanishing degree 2 cohomology,” Pac. J. Math., 48, 403-422 (1973).

    Article  MathSciNet  Google Scholar 

  17. D. O. Revin, “The Dπ-property in finite groups for 2 ∉ π,” Trudy Inst. Mat. Mekh. UrO RAN, 13, No. 1, 166-182 (2007).

    Google Scholar 

  18. J. G. Thompson, “Normal p-complements for finite groups,” J. Alg., 1, 43-46 (1964).

    Article  MathSciNet  Google Scholar 

  19. M. I. Kargapolov and Yu. I. Merzlyakov, Fundamentals of Group Theory [in Russian], 3d edn., Nauka, Moscow (1982).

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Correspondence to A. V. Vasil’ev.

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Supported by Russian Science Foundation, project No. 19-11-00039.

Translated from Algebra i Logika, Vol. 59, No. 1, pp. 3-26, January-February, 2020.

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Vasil’ev, A.V. Normalizers of Sylow Subgroups in Finite Linear and Unitary Groups. Algebra Logic 59, 1–17 (2020). https://doi.org/10.1007/s10469-020-09575-y

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