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Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.2020.tde-19112020-022004
Document
Author
Full name
Vitor Araujo Garcia
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2020
Supervisor
Committee
Ferraz, Raul Antonio (President)
Kitani, Patrícia Massae
Milies, Francisco Cesar Polcino
Paques, Antonio
Taufer, Edite
Title in Portuguese
Unidades centrais em anéis de grupo
Keywords in Portuguese
Anel de grupo
Anel de grupo integral
Grupos abelianos elementares
Grupos diedrais generalizados
Grupos metabelianos
Lema de Kümmer
Primos regulares
Unidades centrais
Abstract in Portuguese
Este trabalho tem como objetivo estudar a estrutura do grupo de unidades centrais de certos anéis de grupo integrais, utilizando principalmente as ideias usadas em um artigo publicado em 2016 (Ferraz e Simón, 2016). Também estudamos o grupo de unidades dos anéis de grupo Z [p] A, onde p é uma raiz primitiva da unidade de ordem p e A é grupo abeliano nito, especialmente quando A tem expoente p.
Title in English
Central units in group rings
Keywords in English
Central units
Elementar abelian groups
Generalized dihedral groups
Group ring
Integral group ring
Kümmer's lemma
Metabelian groups
Regular primes
Abstract in English
The goal of this work is to study the group of central units of certain integral group rings, mainly using the ideas presented in an article from 2016 (Ferraz and Simón, 2016). We also studied the group of units of the group ring Z [p] A, where p is a primitive p-root of unity and A is a nite abelian group, specially when the exponent of A is p
 
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Publishing Date
2021-01-20
 
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