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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).

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

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