Fittingmengen und lockettabschnitte

Abstract The theory of Lockett sections is transferred from Fitting classes to Fitting sets. This in general works only partially; in some special groups (which I call “mobility” groups), however, among these the stable linear groups, a literal translation of the Fitting class theory is possible. As the groups relevant in outer Fitting pairs actually are mobility groups, a new way of deriving information on the Lockett section of a Fitting class arises. This is used to present a simplified, if nonsoluble, counter-example to Lockett's conjecture and to decide a related question. Also, an approach to generating Fitting classes is given.

Allgemeines Über Äussere Fittingpaare

AbstractWe discuss some general properties and limitations of the concept of outer Fitting pairs introduced earlier by the author. We describe an outer Fitting pair as a co-cone in the category of what we call outer groups (roughly speaking the category of groups modulo inner automorphisms). It is shown that generally no universal outer Fitting pair exists, whence this category is not co-complete. Additionally it is shown that if the target group of an outer Fitting pair is finite, then the much more amenable concept of normal Fitting pairs (that is, co-cones in the category of groups) applies.

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