Módulos de permutação p-ádicos para p-grupos abelianos elementares
Let $\Z_p$ be the ring of $p$-adic integers and $G$ be a finite $p$-group. Recently, MacQuarrie and Zalesskii characterized the $\Z_pG$-permutation modules by just looking at modules for $G/N$, where $N$ is a normal subgroup of $G$ with order $p$. This characterization is given by two conditions and...
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| Tipo de recurso: | tesis de maestría |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | Brasil |
| Institución: | Universidade Federal de Minas Gerais (UFMG) |
| Repositorio: | Repositório Institucional da UFMG |
| Idioma: | portugués |
| OAI Identifier: | oai:repositorio.ufmg.br:1843/43922 |
| Acceso en línea: | http://hdl.handle.net/1843/43922 |
| Access Level: | acceso abierto |
| Palabra clave: | Módulos de permutação p-grupos finitos Matemática – Teses Módulos (Álgebra) – Teses Grupos finitos– Teses |
| Sumario: | Let $\Z_p$ be the ring of $p$-adic integers and $G$ be a finite $p$-group. Recently, MacQuarrie and Zalesskii characterized the $\Z_pG$-permutation modules by just looking at modules for $G/N$, where $N$ is a normal subgroup of $G$ with order $p$. This characterization is given by two conditions and in this work we show that, in general, we cannot remove either of these conditions to characterize the permutation $\Z_pG$-modules. The authors already knew that one of the conditions could not be removed but the necessity of the other condition was unknown. We work with a correspondence due to Butler to construct a $\Z_pG$-module that is not a $\Z_pG$-permutation module, but which satisfies the condition that might still have been a characterization of permutation $\Z_pG$-modules. |
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