Group in which every endomorphism is trivial or an automorphism

Definition
A group in which every endomorphism is trivial or an automorphism is a (typically, nontrivial) group for which every endomorphism is either the trivial map (sending all group elements to the identity element) or is an automorphism.

Whether the trivial group is included or not is a matter of convention. We sometimes exclude it when comparing with other simple group-type properties.

Stronger properties

 * Weaker than::Finite simple group:
 * Weaker than::Finite quasisimple group:
 * Weaker than::Simple co-Hopfian group:

Weaker properties

 * Stronger than::Directly indecomposable group
 * Stronger than::Splitting-simple group:
 * Stronger than::Hopfian group
 * Stronger than::co-Hopfian group