Block theory and Brauer's first main theorem for profinite groups
| Autor: | Flores, Ricardo J. Franquiz, MacQuarrie, John W. |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We develop the local-global theory of blocks for profinite groups. Given a field $k$ of characteristic $p$ and a profinite group $G$, one may express the completed group algebra $k[[G]]$ as a product $\prod_{i\in I}B_i$ of closed indecomposable algebras, called the blocks of $G$. To each block $B$ of $G$ we associate a pro-$p$ subgroup of $G$, called the defect group of $B$, unique up to conjugacy in $G$. We give several characterizations of the defect group in analogy with defect groups of blocks of finite groups. Our main theorem is a Brauer correspondence between the blocks of $G$ with defect group $D$ and the blocks of the normalizer $N_G(D)$ with defect group $D$. Comment: 25 pages. Final version, to be published in Advances in Mathematics |
| Databáze: | arXiv |
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