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COMPLETE EMBEDDINGS OF GROUPS
Published online by Cambridge University Press: 26 January 2024
Abstract
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.
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- Research Article
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- Copyright
- © The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.
Footnotes
For our friend and coauthor Chuck Miller in his ninth decade, with deep respect and affection