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arXiv · 2312.08913

Complete Embeddings of Groups

Martin R. Bridson·Hamish Short
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Abstract

Every countable group $G$ can be embedded in a finitely generated group $G^*$ that is hopfian and complete, i.e. $G^*$ 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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Martin R. Bridson, Hamish Short. 2023-12-14. Complete Embeddings of Groups. https://doi.org/10.1017/s0004972723001442

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