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Submaximal and Epimaximal Ӿ -Subgroups

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Algebra and Logic Aims and scope

We discuss how meaningful is the concept of an epimaximal Ӿ -subgroup dual to the concept of a submaximal Ӿ -subgroup introduced by H. Wielandt. Also a result of Wielandt is refined which characterizes the behavior of maximal Ӿ -subgroups under homomorphisms.

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References

  1. O. Hölder, “Bildung zusammengesetzter Gruppen,” Math. Ann., 46, 321-422 (1895).

    Article  MathSciNet  Google Scholar 

  2. W. Guo and D. O. Revin, “Maximal and submaximal Ӿ -subgroups,” Algebra and Logic, Vol. 57, No. 1, 9-28 (2018).

    Article  MathSciNet  Google Scholar 

  3. H. Wielandt, “Zusammengesetzte Gruppen: Holders Programm heute,” in Proc. Symp. Pure Math., 37, Am. Math. Soc., Providence, RI (1980), pp. 161-173.

  4. H. Wielandt, “Zusammengesetzte Gruppen endlicher Ordnung. Vorlesung an der Univ. Tübingen im Wintersemester 1963/64,” in H. Wielandt, Mathematische Werke. Mathematical Works, Vol. 1, Group Theory, B. Huppert and H. Schneider (Eds.), Walter de Gruyter, Berlin (1994), pp. 607-655.

  5. W. Guo and D. O. Revin, “Conjugacy of maximal and submaximal Ӿ -subgroups,” Algebra and Logic, 57, No. 3, 169-181 (2018).

    Article  MathSciNet  Google Scholar 

  6. W. Guo, D. O. Revin, and E. P. Vdovin, “Finite groups in which the Ӿ -maximal subgroups are conjugate,” arXiv:1808.10107 [math.GR].

  7. P. Hall, “Theorems like Sylow’s,” Proc. London Math. Soc., III. Ser., 6, No. 22, 286-304 (1956).

    Article  MathSciNet  Google Scholar 

  8. D. Revin, S. Skresanov, and A. Vasil’ev, “The proper definition and Wielandt–Hartley’s theorem for submaximal Ӿ -subgroups,” Mon. Math., arXiv:1910.09785 [math.GR].

  9. W. Guo and D. O. Revin, “Classification and properties of the π-submaximal subgroups in minimal nonsolvable groups,” Bull. Math. Sci., 8, No. 2, 325-351 (2018).

    Article  MathSciNet  Google Scholar 

  10. W. Guo and D. O. Revin, “Pronormality and submaximal Ӿ -subgroups on finite groups,” Comm. Math. Stat., 6, No. 3, 289-317 (2018).

    Article  MathSciNet  Google Scholar 

  11. I. N. Belousov and M. S. Nirova, Trudy Inst. Mat. Mekh. UrO RAN, 25, No. 4, 283-287 (2019).

    Article  Google Scholar 

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    D. O. Revin

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  1. D. O. Revin
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Correspondence to D. O. Revin.

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Supported by SB RAS Fundamental Research Program I.1.1, project No. 0314-2016-0001.

Translated from Algebra i Logika, Vol. 58, No. 6, pp. 714-719, November-December, 2019.

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Revin, D.O. Submaximal and Epimaximal Ӿ -Subgroups. Algebra Logic 58, 475–479 (2020). https://doi.org/10.1007/s10469-020-09567-y

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  • DOI: https://doi.org/10.1007/s10469-020-09567-y

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