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...

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Detalles Bibliográficos
Autores: Garaialde Ocaña, Oihana, González Sánchez, Jon, Guerrero Sánchez, Lander
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
Descripción
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.