Auflösbarkeit von Gruppen, deren Untergruppen alle subnormal sind. (Solubility of groups all subgroups of which are subnormal) (Q1114002)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Auflösbarkeit von Gruppen, deren Untergruppen alle subnormal sind. (Solubility of groups all subgroups of which are subnormal) |
scientific article; zbMATH DE number 4083908
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Auflösbarkeit von Gruppen, deren Untergruppen alle subnormal sind. (Solubility of groups all subgroups of which are subnormal) |
scientific article; zbMATH DE number 4083908 |
Statements
Auflösbarkeit von Gruppen, deren Untergruppen alle subnormal sind. (Solubility of groups all subgroups of which are subnormal) (English)
0 references
1990
0 references
A proof is given that a group with all subgroups subnormal is soluble. This is a generalization of a theorem of C. Casolo which says that the derived series of such a group ends after a finite number of steps. Moreover it is shown that the Fitting subgroup of a group with all subgroups subnormal contains its torsion subgroup.
0 references
derived series
0 references
Fitting subgroup
0 references
torsion subgroup
0 references
groups with all subgroups subnormal
0 references
solubility of groups
0 references
