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On \( \sigma \)-Subnormality of Sylow Subgroups in a Finite Group

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Abstract

Given an arbitrary partition \( \sigma \) of the set of primes, we give some criteria for the \( \sigma \)-subnormality of a Sylow subgroup of a finite group.

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References

  1. Wielandt H., “Kriterien für Subnormalität in endlichen Gruppen,” Math. Z., vol. 138, no. 3, 199–203 (1974).

    Article  MathSciNet  Google Scholar 

  2. Skiba A. N., “On \( \sigma \)-subnormal and \( \sigma \)-permutable subgroups of finite groups,” J. Algebra, vol. 436, 1–16 (2015).

    Article  MathSciNet  Google Scholar 

  3. Wielandt H., “Eine Verallgemeinerung der invarianten Untergruppen,” Math. Z., vol. 45, 209–244 (1939).

    Article  MathSciNet  Google Scholar 

  4. Kamornikov S. F. and Tyutyanov V. N., “A criterion for the \( \sigma \)-subnormality of a subgroup in a finite \( 3^{\prime} \)-group,” Russian Math. (Iz. VUZ), vol. 8, 36–43 (2020).

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  6. Wilson R. A., Maximal Subgroups of Sporadic Groups. arXiv:1701.02095v2 [math.GR] (2017).

    Book  Google Scholar 

  7. Doerk K. and Hawkes T., Finite Soluble Groups, De Gruyter, Berlin and New York (1992).

    Book  Google Scholar 

  8. Skiba A. N., “On some results in the theory of finite partially soluble groups,” Commun. Math. Stat., vol. 4, no. 3, 281–309 (2016).

    Article  MathSciNet  Google Scholar 

  9. Kamornikov S. F., “Permutability of subgroups and \( \mathfrak{F} \)-subnormality,” Sib. Math. J., vol. 37, no. 5, 936–949 (1996).

    Article  MathSciNet  Google Scholar 

  10. Ballester-Bolinches A. and Ezquerro L. M., Classes of Finite Groups, Springer, New York (2006).

    MATH  Google Scholar 

  11. Wiegold J. and Williamson A. G., “The factorization of the alternating and symmetric groups,” Math. Z., vol. 175, 171–179 (1980).

    Article  MathSciNet  Google Scholar 

  12. Wielandt H., Finite Permutation Groups, Academic, New York (1964).

    MATH  Google Scholar 

  13. Guest S. and Levy D., “Criteria for solvable radical membership via \( p \)-elements,” J. Algebra, vol. 415, 88–111 (2014).

    Article  MathSciNet  Google Scholar 

  14. Huppert B., Endliche Gruppen. I, Springer, Berlin, Heidelberg, and New York (1967).

    Book  Google Scholar 

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

    Book  Google Scholar 

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Funding

S. F. Kamornikov was supported by the Ministry of Education of the Republic of Belarus (Grant GR 20191056). The first two authors were supported by the RFBR and BRFFR (Project F20R–291).

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Correspondence to S. F. Kamornikov.

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Translated from Sibirskii Matematicheskii Zhurnal, 2021, Vol. 62, No. 2, pp. 286–297. https://doi.org/10.33048/smzh.2021.62.204

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Kamornikov, S.F., Tyutyanov, V.N. & Shemetkova, O.L. On \( \sigma \)-Subnormality of Sylow Subgroups in a Finite Group. Sib Math J 62, 230–238 (2021). https://doi.org/10.1134/S003744662102004X

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  • DOI: https://doi.org/10.1134/S003744662102004X

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