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Nonabelian Composition Factors of a Finite Group Whose Maximal Subgroups of Odd Indices Are Hall Subgroups

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Abstract

We obtain a description of nonabelian composition factors of a finite nonsolvable group in which any maximal subgroup of odd index is a Hall subgroup.

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References

  1. E. P. Vdovin and D. O. Revin, “Sylow-type theorems,” Russ. Math. Surv. 66 (5), 829–870 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  2. A. S. Kondrat’ev, Lie Groups and Algebras (IMM UrO RAN, Yekaterinburg, 2009) [in Russian].

    Google Scholar 

  3. A. S. Kondrat’ev, “Normalizers of the Sylow 2-subgroups in finite simple groups,” Math. Notes 78 (3), 338–346 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  4. A. S. Kondrat’ev, “Subgroups of finite Chevalley groups,” Russ. Math. Surv. 41 (1), 65–118 (1986).

    Article  MathSciNet  MATH  Google Scholar 

  5. The Kourovka Notebook: Unsolved Problems in Group Theory, 18th ed. (Inst. Mat. SO RAN, Novosibirsk, 2014). http://math.nsc.ru/|alglog/18kt.pdf

  6. N. V. Maslova, “Classification of maximal subgroups of odd index in finite simple classical groups,” Proc. Steklov Inst. Math. 267 (Suppl. 1), S164–S183 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  7. N. V. Maslova, “Classification of maximal subgroups of odd index in finite groups with alternating socle,” Proc. Steklov Inst. Math. 285 (Suppl. 1), S136–S138 (2014).

    Article  MATH  Google Scholar 

  8. N. V. Maslova, “Maximal subgroups of odd index in finite groups with simple linear, unitary, or symplectic socle,” Algebra Logic 50 (2), 133–145 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  9. N. V. Maslova, “Nonabelian composition factors of a finite group whose all maximal subgroups are Hall,” Sib. Math. J. 53 (5), 853–861 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  10. N. V. Maslova and D. O. Revin, “Finite groups whose maximal subgroups have the Hall property,” Sib. Adv. Math. 23 (3), 196–209 (2013).

    Article  MATH  Google Scholar 

  11. V. S. Monakhov, “Finite π-solvable groups whose maximal subgroups have the Hall property,” Math. Notes 84 (3–4), 363–366 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  12. D. O. Revin, “Hall π-subgroups of finite Chevalley groups whose characteristic belongs to π,” Sib. Adv. Math. 9 (2), 25–71 (1999).

    MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  14. J. N. Bray, D. F. Holt, and C. M. Roney-Dougal, The Maximal Subgroups of the Low-Dimensional Finite Classical Groups (Cambridge Univ. Press, Cambridge, 2013).

    Book  MATH  Google Scholar 

  15. M. Giudici, “Maximal subgroups of almost simple groups with socle PSL(2, q).” https://arxiv.org/abs /math/0703685.pdf. Cited March 23, 2007.

    Google Scholar 

  16. P. Hall, “Theorems like Sylow’s,” Proc. London Math. Soc. (3) 6 (2), 286–304 (1956).

    Article  MathSciNet  MATH  Google Scholar 

  17. P. Kleidman and M. Liebeck, The Subgroup Structure of the Finite Classical Groups (Cambridge Univ. Press, Cambridge, 1990).

    Book  MATH  Google Scholar 

  18. M. W. Liebeck and J. Saxl, “The primitive permutation groups of odd degree,” J. London Math. Soc. 31 (2), 250–264 (1985).

    Article  MathSciNet  MATH  Google Scholar 

  19. T. Oshima, “A classification of subsystems of a root system,” http://arxiv.org/pdf/math/0611904v4.pdf. Cited June 14, 2007.

    Google Scholar 

  20. D. O. Revin and E. P. Vdovin, “On the number of classes of conjugate Hall subgroups in finite simple groups,” J. Algebra 324, 3614–3652 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  21. J. G. Thompson, “Hall subgroups of the symmetric groups,” J. Comb. Theory 1, 271–279 (1966).

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to N. V. Maslova.

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Original Russian Text © N.V.Maslova, D.O. Revin, 2016, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2016, Vol. 22, No. 3.

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Maslova, N.V., Revin, D.O. Nonabelian Composition Factors of a Finite Group Whose Maximal Subgroups of Odd Indices Are Hall Subgroups. Proc. Steklov Inst. Math. 299 (Suppl 1), 148–157 (2017). https://doi.org/10.1134/S0081543817090176

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  • DOI: https://doi.org/10.1134/S0081543817090176

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