A Generalization of an Important Result of Bryce and Cossey

Chi ZHANG, Zhen Feng WU

Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (3) : 415-422.

PDF(434 KB)
PDF(434 KB)
Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (3) : 415-422. DOI: 10.12386/A2022sxxb0033

A Generalization of an Important Result of Bryce and Cossey

  • Chi ZHANG1, Zhen Feng WU2
Author information +
History +

Abstract

In the theory of formations of finite soluble groups, Bryce and Cossey proved an important theorem: A soluble local formation F is a Fitting class if and only if every value of the canonical formation function F of F is a Fitting class. In this paper, basing on the theory of σ-groups, we generalized the results of Bryce and Cossey. We proved that A σ-local formation F is a Fitting class if and only if every value of the canonical σ-local definition F of F is a Fitting class.

Key words

theory of σ-groups / σ-soluble groups / σ-local formations / Fitting classes

Cite this article

Download Citations
Chi ZHANG, Zhen Feng WU. A Generalization of an Important Result of Bryce and Cossey. Acta Mathematica Sinica, Chinese Series, 2022, 65(3): 415-422 https://doi.org/10.12386/A2022sxxb0033

References

[1] Ballester-Bolinches A., Calvo Clara, Esteban-Romero R., Products of formations of finite groups, Journal of Algebra, 2006, 29(2): 602–615.
[2] Ballester-Bolinches A., Ezquerro L. M., Classes of Finite Groups, Springer-Verlag, Dordrecht, 2006.
[3] Bryce R. A., Cossey J., Fitting formations of finite soluble groups, Math. Z., 1972, 127: 217–223.
[4] Cater R., On a class of finite solvable groups, Pro. London Math. Soc., 1959, 9(3): 623–640.
[5] Doerk K., Hawkes T., Finite Soluble Groups, Walter de Gruyter, Berlin, 1992.
[6] Gaschütz, Zur Theorie der endlichen auflösbaren Gruppen, Math. Z., 1962/1963, 80: 300–305.
[7] Guo W. B., The Theory of Classes of Groups, Science Press, Kluwer Academic Publishers, Beijing, New York, Dordrecht, Boston, London, 2000.
[8] Guo W. B., Structure Theory for Canonical Classes of Finite Groups, Springer, New York, London, 2015.
[9] Guo W. B., Skiba A. N., Finite groups with permutable complete Wielandt sets of subgroups, J. Group Theory, 2015, 18: 191–200.
[10] Guo W. B., Skiba A. N., Finite groups whose n-maximal subgroups are σ-subnormal, Sci. China Math., 2019, 62(7): 1355–1372.
[11] Guo W. B., Zhang L., Vorob’ev N. T., On σ-local Fitting classes, Journal of Algebra, 2020, 542: 116–129.
[12] Skiba A. N., On sublattices of the subgroup lattice defined by formation Fitting sets, J. Algebra, 2020, 550: 69–85.
[13] Skiba A. N., On σ-subnormal and σ-permutable subgroups of finite groups, J. Algebra, 2015, 436: 1–16.
[14] Skiba A. N., Some characterizations of finite σ-soluble PσT -groups, J. Algebra, 2018, 495: 114–129.
[15] Tang J. P., Zhang J., Miao L., New criteria for quasi-F-groups, Commun. Math. Stat., 2019, 7(1): 25–32.
[16] Yang N. Y., Li B. J., Vorob’ev N. T., On the dual theory of a result of Bryce and Cossey, J. Algebra, 2019, 522: 124–133.
[17] Zhang C., Skiba A. N., On Σtσ -closed classes of finite groups, Ukrainian Math. J., 2019, 70(12): 1966–1977.
PDF(434 KB)

421

Accesses

0

Citation

Detail

Sections
Recommended

/