Profinite Direct Sums with Applications to Profinite Groups of Type $Φ_R$
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917062058704896 |
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| author | Tang, Jiacheng |
| author_facet | Tang, Jiacheng |
| contents | We show that the "profinite direct sum" is a good notion of infinite direct sums for profinite modules having properties similar to direct sums of abstract modules. For example, the profinite direct sum of projective modules is projective, and there is a Mackey's Formula for profinite modules described using these sums. As an application, we prove that the class of profinite groups of type $Φ_R$ is closed under subgroups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05182 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Profinite Direct Sums with Applications to Profinite Groups of Type $Φ_R$ Tang, Jiacheng Rings and Algebras Category Theory Group Theory 20E18, 16E30, 18F10 We show that the "profinite direct sum" is a good notion of infinite direct sums for profinite modules having properties similar to direct sums of abstract modules. For example, the profinite direct sum of projective modules is projective, and there is a Mackey's Formula for profinite modules described using these sums. As an application, we prove that the class of profinite groups of type $Φ_R$ is closed under subgroups. |
| title | Profinite Direct Sums with Applications to Profinite Groups of Type $Φ_R$ |
| topic | Rings and Algebras Category Theory Group Theory 20E18, 16E30, 18F10 |
| url | https://arxiv.org/abs/2504.05182 |