Conjugacy in Miller's Groups
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909345091944448 |
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| author | Gillis, Conan |
| author_facet | Gillis, Conan |
| contents | In 1971 C.F.\ Miller associated to every finitely presented group $G$ a free-by-free group $M(G)$ known as the Miller Machine, whose conjugacy problem is closely related to the conjugacy and word problems of $G$. We quantify this relationship, and look to fully understand the conjugacy problem of $M(G)$; namely, we reduce the conjugacy problem in $M(G)$ to a strong form of list conjugacy in $G$, which we term iso-computational list conjugacy. As an application, we show that if $G$ is finite, the conjugacy problem for $M(G)$ is in $\mathsf{PSPACE}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08869 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conjugacy in Miller's Groups Gillis, Conan Group Theory In 1971 C.F.\ Miller associated to every finitely presented group $G$ a free-by-free group $M(G)$ known as the Miller Machine, whose conjugacy problem is closely related to the conjugacy and word problems of $G$. We quantify this relationship, and look to fully understand the conjugacy problem of $M(G)$; namely, we reduce the conjugacy problem in $M(G)$ to a strong form of list conjugacy in $G$, which we term iso-computational list conjugacy. As an application, we show that if $G$ is finite, the conjugacy problem for $M(G)$ is in $\mathsf{PSPACE}$. |
| title | Conjugacy in Miller's Groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2401.08869 |