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Groups sharing some varietal properties with supersoluble groups

Part of: Representation theory of groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Rolf Brandl
Rolf Brandl
Affiliation:
Mathematisches InstitutAm Hubland12 D-8700 Würzburg, Germany
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Abstract

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In this note a formation U is considered which can be defined by a sequence of laws which ‘almost’ hold in every finite supersoluble group. The class U contains all finite supersoluble groups and each group in U has a Sylow tower.

It is shown that a finite group belongs to U if and only if all of its subgroups with nilpotent commutator subgroup are supersoluble. A more general result concerning classes of this type finally proves that U is a saturated formation.

MSC classification

Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks 20F16: Solvable groups, supersolvable groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 34 , Issue 2 , April 1983 , pp. 265 - 268
Copyright
Copyright © Australian Mathematical Society 1983

References

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