A family of finite p-groups satisfying Carlson's depth conjecture
Let p > 3 be a prime number and let r be an integer with 1 < r < p - 1. For each r, let moreover G(r) denote the unique quotient of the maximal class pro-p group of size p(r+1).We show that the mod-p cohomology ring of G(r) has depth one and that, in turn, it satisfies the equalities in Car...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad del País Vasco |
| Repositorio: | Addi. Archivo Digital para la Docencia y la Investigación |
| OAI Identifier: | oai:addi.ehu.eus:10810/57894 |
| Acceso en línea: | http://hdl.handle.net/10810/57894 |
| Access Level: | acceso abierto |
| Palabra clave: | depth finite p-groups mod-p cohomology ring |
| Sumario: | Let p > 3 be a prime number and let r be an integer with 1 < r < p - 1. For each r, let moreover G(r) denote the unique quotient of the maximal class pro-p group of size p(r+1).We show that the mod-p cohomology ring of G(r) has depth one and that, in turn, it satisfies the equalities in Carlson's depth conjecture [2]. This is the first family of finite p-groups for which Carlson's depth conjecture has been verified besides p-groups of abelian type mod-p cohomology or extraspecial p-groups. Moreover, this computation is possible without first describing the structure of the cohomology ring. |
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