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- Fittings_theorem abstract "Fitting's theorem is a mathematical theorem proved by Hans Fitting. It can be stated as follows:If M and N are nilpotent normal subgroups of a group G, then their product MN is also a nilpotent normal subgroup of G; if, moreover, M is nilpotent of class m and N is nilpotent of class n, then MN is nilpotent of class at most m + n.By induction it follows also that the subgroup generated by a finite collection of nilpotent normal subgroups is nilpotent. This can be used to show that the Fitting subgroup of certain types of groups (including all finite groups) is nilpotent. However, a subgroup generated by an infinite collection of nilpotent normal subgroups need not be nilpotent.".
- Fittings_theorem wikiPageID "4081611".
- Fittings_theorem wikiPageLength "1633".
- Fittings_theorem wikiPageOutDegree "13".
- Fittings_theorem wikiPageRevisionID "555571940".
- Fittings_theorem wikiPageWikiLink Category:Theorems_in_group_theory.
- Fittings_theorem wikiPageWikiLink Complete_lattice.
- Fittings_theorem wikiPageWikiLink Finite_group.
- Fittings_theorem wikiPageWikiLink Fitting_subgroup.
- Fittings_theorem wikiPageWikiLink Group_(mathematics).
- Fittings_theorem wikiPageWikiLink Hans_Fitting.
- Fittings_theorem wikiPageWikiLink Lattice_of_subgroups.
- Fittings_theorem wikiPageWikiLink Mathematical_induction.
- Fittings_theorem wikiPageWikiLink Mathematics.
- Fittings_theorem wikiPageWikiLink Nilpotent_group.
- Fittings_theorem wikiPageWikiLink Normal_subgroup.
- Fittings_theorem wikiPageWikiLink Order_theory.
- Fittings_theorem wikiPageWikiLink Theorem.
- Fittings_theorem wikiPageWikiLinkText "Fitting's theorem".
- Fittings_theorem hasPhotoCollection Fittings_theorem.
- Fittings_theorem wikiPageUsesTemplate Template:Abstract-algebra-stub.
- Fittings_theorem wikiPageUsesTemplate Template:PlanetMath.
- Fittings_theorem subject Category:Theorems_in_group_theory.
- Fittings_theorem hypernym Theorem.
- Fittings_theorem comment "Fitting's theorem is a mathematical theorem proved by Hans Fitting. It can be stated as follows:If M and N are nilpotent normal subgroups of a group G, then their product MN is also a nilpotent normal subgroup of G; if, moreover, M is nilpotent of class m and N is nilpotent of class n, then MN is nilpotent of class at most m + n.By induction it follows also that the subgroup generated by a finite collection of nilpotent normal subgroups is nilpotent.".
- Fittings_theorem label "Fitting's theorem".
- Fittings_theorem sameAs Teorema_de_Fitting.
- Fittings_theorem sameAs m.0bh2kj.
- Fittings_theorem sameAs Q5455495.
- Fittings_theorem sameAs Q5455495.
- Fittings_theorem sameAs 菲廷定理.
- Fittings_theorem wasDerivedFrom Fittings_theoremoldid=555571940.
- Fittings_theorem isPrimaryTopicOf Fittings_theorem.