Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-04T21:56:35.247Z Has data issue: false hasContentIssue false
  • English
  • Français

The p-Huppert-subgroup and the set of p-quasi-superfluous elements in a finite group

Published online by Cambridge University Press:  20 January 2009

Angel Carocca  and
Rudolf Maier
Angel Carocca
Affiliation:
Universidade de Brasilia, Departamento de Matemática-IE, 70.910 Brasilia-D.F., Brazil E-Mail: MAIERR @ BRUNB
Rudolf Maier
Affiliation:
Universidade de Brasilia, Departamento de Matemática-IE, 70.910 Brasilia-D.F., Brazil E-Mail: MAIERR @ BRUNB
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Based on the theory of p-supersoluble and supersoluble groups, a prime-number parametrized family of canonical characteristic subgroups Γp(G) and their intersection Γ(G) is introduced in every finite group G and some of its properties are studied. Special interest is dedicated to an elementwise description of the largest p-nilpotent normal subgroup of Γp(G) and of the Fitting subgroup of Γ(G).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 36 , Issue 2 , June 1993 , pp. 289 - 297
Copyright
Copyright © Edinburgh Mathematical Society 1993

References

REFERENCES

1.Bhatia, H. C., A Generalized Frattini Subgroup of a Finite Group (Ph.D. thesis, Michigan State Univ., East Lansing, 1972).Google Scholar
2.Feng, Y.-Q. and Zhang, B.-L., Frattini subgroup relative to formation functions, J. Pure Appl. Algebra 64 (1990), 145–148.CrossRefGoogle Scholar
3.Gaschütz, W., Über die Φ-Untergruppe endlicher Gruppen, Math. Z. 58 (1953), 160–170.CrossRefGoogle Scholar
4.Huppert, B., Endliche Gruppen I (Springer-Verlag, Berlin, Heidelberg, New York, 1967).CrossRefGoogle Scholar
5.Huppert, B., Normalteiler und maximale Untergruppen endlicher Gruppen, Math. Z. (1954), 409–434.CrossRefGoogle Scholar
6.Maier, R., Zur Vertauschbarkeit und Subnormalität von Untergruppen, Arch. Math. (1989), 110–120.CrossRefGoogle Scholar
7.Maier, R., Faktorisierte p-auflösbare Gruppen, Arch. Math. 27 (1976), 576–583.CrossRefGoogle Scholar
8.Ritt, I. F., On algebraic functions which can be expressed in terms of radicals, Trans. Amer. Math.Soc. 24 (1923), 21–30.CrossRefGoogle Scholar