Complete Embeddings of Groups
| Autor: | Bridson, Martin R., Short, Hamish |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Bull. Aust. Math. Soc. 110 (2024) 136-144 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1017/S0004972723001442 |
| Popis: | 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. Comment: 9 pages, 1 figure. Dedicated to Chuck Miller. To appear in the Bulletin of the Australian Mathematical Society |
| Databáze: | arXiv |
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