Characteristically Hopfian group

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A group G is termed a characteristically Hopfian group if there is no nontrivial characteristic subgroup H of G for which the quotient group G/H is isomorphic to G.

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Hopfian group