Fitting functors in finite solvable groups: II
Published online by Cambridge University Press: 24 October 2008
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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