Finite group in which every endomorphism is trivial or an automorphism

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

Stronger properties

 * Weaker than::Finite simple group:
 * Weaker than::Finite quasisimple group: