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Allgemeines Über Äussere Fittingpaare

Part of: Special categories Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Joachim Pense
Joachim Pense
Affiliation:
Fachbereich MathematikJohannes Gutenberg-UniversitätD-6500 Mainz, Federal Republic of Germany
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Abstract

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We 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.

MSC classification

Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks 18B99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 49 , Issue 2 , October 1990 , pp. 241 - 249
Copyright
Copyright © Australian Mathematical Society 1990

References

Literatur

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