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Fitting functors in finite solvable groups: II

Published online by Cambridge University Press:  24 October 2008

James C. Beidleman ,
Ben Brewster  and
Peter Hauck
James C. Beidleman
Affiliation:
Department of Mathematics, University of Kentucky, Lexington, KY 40506, U.S.A.
Ben Brewster
Affiliation:
Department of Mathematical Sciences, State University of New York, Binghamton, NY 13901, U.S.A.
Peter Hauck
Affiliation:
Mathematisches Institut, Albert-Ludwigs-Universität, D 7800 Freiburg, West Germany
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Extract

This paper is a continuation of [1], where we introduced the concept and investigated the basic properties of Fitting functors for finite solvable groups. We recall that a map f which assigns to each finite solvable group G a non-empty set f(G) of subgroups of G is called a Fitting functor if the following property is satisfied: whenever α: G → H is a monomorphism with α(G) ⊴ H, then

The most prominent examples of conjugate Fitting functors are provided by injectors of Fitting classes. However, Fitting functors f in general do not behave as nicely as injectors. For instance, f(G) need not consist of pronormal subgroups of a group G (cf. [1], 4·3).

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 101 , Issue 1 , January 1987 , pp. 37 - 55
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

REFERENCES

[1]Beidleman, J. C., Brewster, B. and Hauck, P.. Fittingfunktoren in endlichen auflösbaren Gruppen I. Math. Z. 182 (1983), 359–384.CrossRefGoogle Scholar
[2]Brison, O. J.. Hall operators for Fitting classes. Arch. Math. 33 (1979), 1–9.CrossRefGoogle Scholar
[3]Doerk, K. and Porta, M.. Über Vertauschbarkeit, normale Einbettung und Dominanz bei Fittingklassen endlicher auflösbarer Gruppen. Arch. Math. 35 (1980), 319–327.CrossRefGoogle Scholar
[4]Hartley., B.On Fischer's dualization of formation theory. Proc. London Math. Soc. (3) 19 (1969), 193–207.CrossRefGoogle Scholar
[5]Hauck., P.On products of Fitting classes. J. London Math. Soc. (2) 20 (1979), 423–434.CrossRefGoogle Scholar
[6]Lockett., F. P. On the theory of Fitting classes of finite soluble groups. Ph.D. thesis, University of Warwick (1971).Google Scholar
[7]Lockett., F. P.The Fitting class . Math. Z. 137 (1974), 131–136.CrossRefGoogle Scholar