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Three Formations over \(\mathfrak U\)

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Abstract

Three classes of finite groups are investigated in which all metanilpotent subgroups, all subgroups with nilpotent derived subgroup, or all Schmidt subgroups are supersolvable.

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References

  1. B. Huppert, Endliche Gruppen. I (Springer- Verlag, Berlin, 1967).

    Book  Google Scholar 

  2. L. S. Kazarin, “On groups with factorization,” Soviet Math. Dokl. 23 (1), 19–22 (1981).

    MATH  Google Scholar 

  3. A. F. Vasil’ev, T. I. Vasil’eva and V. N. Tyutyanov, “On the finite groups of supersolvable type,” Sib. Math. J. 51 (6), 1004–1012 (2010).

    Article  MathSciNet  Google Scholar 

  4. V. S. Monakhov, “Finite groups with abnormal and \(\mathfrak U\)-subnormal subgroups,” Sib. Math. J. 57 (2), 447–462 (2016).

    Article  MathSciNet  Google Scholar 

  5. V. S. Monakhov, “Finite groups with a given set of Schmidt subgroups,” Math. Notes 58 (5), 1183–1186 (1995).

    Article  MathSciNet  Google Scholar 

  6. O. Yu. Schmidt, “Groups all of whose subgroups are special,” Mat. Sb. 31 (3-4), 366–372 (1924).

    Google Scholar 

  7. L. A. Shemetkov, Formations of Finite Groups. Monographs in Modern Algebra (Nauka, Moscow, 1978) [in Russian].

    Google Scholar 

  8. B. Huppert, “Normalteiler und maximale Untergruppen endlicher Gruppen,” Math. Z. 60, 409–434 (1954).

    Article  MathSciNet  Google Scholar 

  9. K. Doerk, “Minimal nicht überauflösbare, endliche Gruppen,” Math. Z. 91, 198–205 (1966).

    Article  MathSciNet  Google Scholar 

  10. V. T. Nagrebetskii, “On finite minimal nonsupersolvable groups,” in Finite Groups (Nauka i Tekhnika, Minsk, 1975), pp. 104–108 [in Russian].

    MathSciNet  Google Scholar 

  11. The GAP Group: GAP – Groups, Algorithms, and Programming www.gap-system.org, Ver. 4.11.0 released on 29 February 2020.

  12. J. C. Beidleman and H. Heineken, “Minimal non-\(\mathfrak F\)-groups,” Ric. Mat. 58 (1), 33–41 (2009).

    Article  MathSciNet  Google Scholar 

  13. V. N. Tyutyanov and P. V. Bychkov, “On finite groups with minimal \(\mathbb{P}\)-subnormal subgroups,” Problems of Physics, Mathematics and Technics, No. 4 (21), 97–99 (2014).

    MATH  Google Scholar 

  14. V. P. Burichenko, “On groups whose small-order elements generate a small subgroup,” Math. Notes 92 (3), 327–332 (2012).

    Article  MathSciNet  Google Scholar 

  15. P. J. Cameron, R. Solomon, and A. Turull, “Chains of subgroups in symmetric groups,” J. Algebra 127 (2), 340–352 (1989).

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

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Correspondence to V. S. Monakhov.

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Translated from Matematicheskie Zametki, 2021, Vol. 110, pp. 358–367 https://doi.org/10.4213/mzm13063.

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Monakhov, V.S. Three Formations over \(\mathfrak U\). Math Notes 110, 339–346 (2021). https://doi.org/10.1134/S0001434621090042

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  • DOI: https://doi.org/10.1134/S0001434621090042

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