Explicit $K_2$ of certain quotient rings over $\mathbb{Z}[G]$ for $G$ an elementary abelian $p$-group
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911445450489856 |
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| author | Zhang, Yakun |
| author_facet | Zhang, Yakun |
| contents | Let $G$ be an elementary abelian $p$-group. In this paper, we calculate the $K_2$-groups of some quotient rings $\mathbb{Z}[G]/I$ for certain ideals $I \subseteq \mathbb{Z}[G]$ of finite $p$-power index. These results are established through the explicit computation of Dennis-Stein symbols. As an application, we provide a definitive characterization of the relative group $SK_1(\mathbb{Z}[G], p^k\mathbb{Z}[G])$ for any odd prime $p$ and $k \ge 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11210 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Explicit $K_2$ of certain quotient rings over $\mathbb{Z}[G]$ for $G$ an elementary abelian $p$-group Zhang, Yakun K-Theory and Homology 19C20, 16S34, 19C99 Let $G$ be an elementary abelian $p$-group. In this paper, we calculate the $K_2$-groups of some quotient rings $\mathbb{Z}[G]/I$ for certain ideals $I \subseteq \mathbb{Z}[G]$ of finite $p$-power index. These results are established through the explicit computation of Dennis-Stein symbols. As an application, we provide a definitive characterization of the relative group $SK_1(\mathbb{Z}[G], p^k\mathbb{Z}[G])$ for any odd prime $p$ and $k \ge 1$. |
| title | Explicit $K_2$ of certain quotient rings over $\mathbb{Z}[G]$ for $G$ an elementary abelian $p$-group |
| topic | K-Theory and Homology 19C20, 16S34, 19C99 |
| url | https://arxiv.org/abs/2401.11210 |