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COMPLETE EMBEDDINGS OF GROUPS
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 110 / Issue 1 / August 2024
- Published online by Cambridge University Press:
- 26 January 2024, pp. 136-144
- Print publication:
- August 2024
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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.
Inversion is Possible in Groups with no Periodic Automorphisms
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 59 / Issue 1 / February 2016
- Published online by Cambridge University Press:
- 05 June 2015, pp. 11-16
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