We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Every countable group G can be embedded in a finitely generated group 
$G^*$ that is hopfian and complete, that is, 
$G^*$ has trivial centre and every epimorphism 
$G^*\to G^*$ is an inner automorphism. Every finite subgroup of 
$G^*$ is conjugate to a finite subgroup of G. If G has a finite presentation (respectively, a finite classifying space), then so does 
$G^*$. Our construction of 
$G^*$ relies on the existence of closed hyperbolic 3-manifolds that are asymmetric and non-Haken.
