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Co-Hopfian group
From Groupprops
This article defines a group property: a property that can be evaluated to true/false for any given group
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications | | | |
RANDOM GROUP PROPERTY: Slender group: A group where every subgroup is finitely generated.
This is a variation of finiteness (groups)
View a complete list of variations of finiteness (groups) OR read a survey article on varying finiteness (groups)
This property makes sense for infinite groups. For finite groups, it is always true
Contents |
Definition
Symbol-free definition
A group is termed co-Hopfian if it satisfies the following equivalent conditions:
- It is not isomorphic to any proper subgroup
- Every injective endomorphism of the group is an automorphism
Relation with other properties
Stronger properties
Incomparable properties
