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On the normalizer of a Gaschütz system of a finite soluble group

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Abstract

The notion of a Gaschütz system of a finite soluble group was introduced by S. F. Kamornikov in 2008 (this is a set of complements of crowns of pairwise nonisomorphic non-Frattini factors of a chief series of the group). In the present paper, properties of Gaschütz systems are investigated. In particular, we calculate the number of Gaschütz systems in a finite soluble group and prove their conjugacy, obtain a connection between \( \mathfrak{N} \)-prefrattini subgroups and normalizers of Gaschütz systems, and investigate factorizations of the normalizer of a Gaschütz system.

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References

  1. A. Ballester-Bolinches and L. M. Ezquerro, Classes of Finite Groups, Springer, Dordrecht (2006).

    MATH  Google Scholar 

  2. K. Doerk and T. Hawkes, Finite Soluble Groups, Walter de Gruyter, Berlin (1992).

    MATH  Google Scholar 

  3. W. Gaschütz, “Praefrattinigruppen,” Arch. Math., 13, No. 3, 418–426 (1962).

    Article  MATH  Google Scholar 

  4. T. O. Hawkes, “Analogues of prefrattini subgroups,” Proc. Int. Conf. Theory of Groups. Australian Nat. Univ., Canberra, 1965, Gordon and Breach, New York (1967), pp. 145–150.

  5. S. F. Kamornikov, “On prefrattini subgroups of finite soluble groups,” Sib. Mat. Zh., 49, No. 2, 1310–1318 (2008).

    MathSciNet  Google Scholar 

  6. L. A. Shemetkov, Formations of Finite Groups [in Russian], Nauka, Moscow (1978).

    MATH  Google Scholar 

  7. L. A. Shemetkov and A. N. Skiba, Formations of Algebraic Systems [in Russian], Nauka, Moscow (1989).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Francisk Scorina Gomel State University, Gomel, Belarus

    S. F. Kamornikov & L. A. Shemetkov

Authors
  1. S. F. Kamornikov
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  2. L. A. Shemetkov
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Corresponding author

Correspondence to L. A. Shemetkov.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 14, No. 8, pp. 129–136, 2008.

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Kamornikov, S.F., Shemetkov, L.A. On the normalizer of a Gaschütz system of a finite soluble group. J Math Sci 166, 655–660 (2010). https://doi.org/10.1007/s10958-010-9880-6

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  • DOI: https://doi.org/10.1007/s10958-010-9880-6

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