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- Characteristically_simple_group abstract "In mathematics, in the field of group theory, a group is said to be characteristically simple if it has no proper nontrivial characteristic subgroups. Characteristically simple groups are sometimes also termed elementary groups. Characteristically simple is a weaker condition than being a simple group, as simple groups must not have any proper nontrivial normal subgroups, which include characteristic subgroups.A finite group is characteristically simple if and only if it is the direct product of isomorphic simple groups. In particular, a finite solvable group is characteristically simple if and only if it is an elementary abelian group. This does not hold in general for infinite groups; for example, the rational numbers form a characteristically simple group that is not a direct product of simple groups.A minimal normal subgroup of a group G is a nontrivial normal subgroup N of G such that the only proper subgroup of N that is normal in G is the trivial subgroup. Every minimal normal subgroup of a group is characteristically simple. This follows from the fact that a characteristic subgroup of a normal subgroup is normal.".
- Characteristically_simple_group wikiPageID "4966729".
- Characteristically_simple_group wikiPageLength "1554".
- Characteristically_simple_group wikiPageOutDegree "14".
- Characteristically_simple_group wikiPageRevisionID "633979988".
- Characteristically_simple_group wikiPageWikiLink Category:Properties_of_groups.
- Characteristically_simple_group wikiPageWikiLink Characteristic_subgroup.
- Characteristically_simple_group wikiPageWikiLink Direct_product_of_groups.
- Characteristically_simple_group wikiPageWikiLink Elementary_abelian_group.
- Characteristically_simple_group wikiPageWikiLink Group_(mathematics).
- Characteristically_simple_group wikiPageWikiLink Group_theory.
- Characteristically_simple_group wikiPageWikiLink Mathematics.
- Characteristically_simple_group wikiPageWikiLink Normal_subgroup.
- Characteristically_simple_group wikiPageWikiLink Rational_number.
- Characteristically_simple_group wikiPageWikiLink Simple_group.
- Characteristically_simple_group wikiPageWikiLink Solvable_group.
- Characteristically_simple_group wikiPageWikiLink Springer-Verlag.
- Characteristically_simple_group wikiPageWikiLink Springer_Science+Business_Media.
- Characteristically_simple_group wikiPageWikiLinkText "Characteristically simple group".
- Characteristically_simple_group wikiPageWikiLinkText "characteristically simple group".
- Characteristically_simple_group wikiPageWikiLinkText "characteristically simple".
- Characteristically_simple_group hasPhotoCollection Characteristically_simple_group.
- Characteristically_simple_group wikiPageUsesTemplate Template:Abstract-algebra-stub.
- Characteristically_simple_group wikiPageUsesTemplate Template:Citation.
- Characteristically_simple_group subject Category:Properties_of_groups.
- Characteristically_simple_group type Property.
- Characteristically_simple_group comment "In mathematics, in the field of group theory, a group is said to be characteristically simple if it has no proper nontrivial characteristic subgroups. Characteristically simple groups are sometimes also termed elementary groups.".
- Characteristically_simple_group label "Characteristically simple group".
- Characteristically_simple_group sameAs Groupe_caractéristiquement_simple.
- Characteristically_simple_group sameAs Grupa_charakterystycznie_prosta.
- Characteristically_simple_group sameAs m.0cxkfn.
- Characteristically_simple_group sameAs Q3117616.
- Characteristically_simple_group sameAs Q3117616.
- Characteristically_simple_group wasDerivedFrom Characteristically_simple_group?oldid=633979988.
- Characteristically_simple_group isPrimaryTopicOf Characteristically_simple_group.