Coset complexes of $p$-subgroups in finite groups
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910865300652032 |
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| author | Gu, Huilong Meng, Hangyang Guo, Xiuyun |
| author_facet | Gu, Huilong Meng, Hangyang Guo, Xiuyun |
| contents | Let $G$ be a finite group and $p$ be a prime. We denote by $C_p(G)$ the poset of all cosets of $p$-subgroups of $G$. We characterize the homotopy type of the geometric realization $|ΔC_p(G)|$ for $p$-closed groups $G$, which is motivated by K.S.Brown's Question. We will further demonstrate that $χ(C_{p}(G)) \equiv |G|_{p'} (\text{mod} p)$ for any finite group $G$ and any prime $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06379 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coset complexes of $p$-subgroups in finite groups Gu, Huilong Meng, Hangyang Guo, Xiuyun Group Theory 20D15, 20D25 Let $G$ be a finite group and $p$ be a prime. We denote by $C_p(G)$ the poset of all cosets of $p$-subgroups of $G$. We characterize the homotopy type of the geometric realization $|ΔC_p(G)|$ for $p$-closed groups $G$, which is motivated by K.S.Brown's Question. We will further demonstrate that $χ(C_{p}(G)) \equiv |G|_{p'} (\text{mod} p)$ for any finite group $G$ and any prime $p$. |
| title | Coset complexes of $p$-subgroups in finite groups |
| topic | Group Theory 20D15, 20D25 |
| url | https://arxiv.org/abs/2503.06379 |