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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 wikiPageRevisionID "544364501".
- Characteristically_simple_group hasPhotoCollection Characteristically_simple_group.
- Characteristically_simple_group subject Category:Group_theory.
- Characteristically_simple_group subject Category:Properties_of_groups.
- Characteristically_simple_group type Abstraction100002137.
- Characteristically_simple_group type Possession100032613.
- Characteristically_simple_group type PropertiesOfGroups.
- Characteristically_simple_group type Property113244109.
- Characteristically_simple_group type Relation100031921.
- 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 label "Groupe caractéristiquement simple".
- Characteristically_simple_group label "Grupa charakterystycznie prosta".
- 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 sameAs Characteristically_simple_group.
- Characteristically_simple_group wasDerivedFrom Characteristically_simple_group?oldid=544364501.
- Characteristically_simple_group isPrimaryTopicOf Characteristically_simple_group.