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Master's Dissertation
DOI
10.11606/D.45.2016.tde-05102015-225032
Document
Author
Full name
Vitor Araujo Garcia
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2015
Supervisor
Committee
Ferraz, Raul Antonio (President)
Milies, Francisco Cesar Polcino
Paques, Antonio
Title in Portuguese
Idempotentes centrais primitivos em algumas álgebras de grupos
Keywords in Portuguese
Álgebra de grupo
Anel de grupo
Código abeliano
Código minimal
Idempotentes
Abstract in Portuguese
O objetivo do trabalho é apresentar alguns resultados acerca de anéis de grupos e aplicações, segundo o que foi estudado em livros e artigos sobre o assunto. Inicialmente, apresentaremos alguns fatos básicos sobre anéis de grupos, que podem ser encontrados em [5], e em seguida, apresentaremos os resultados principais, mais recentes, que foram estudados em dois artigos diferentes. No primeiro artigo [4], apresentou-se uma forma de calcular o número de componentes simples de certas álgebras de grupos abelianos finitos, bem como também foi apresentada uma forma de calcular geradores idempotentes de códigos abelianos minimais, suas dimensões e seus pesos. No segundo artigo [2], encontra-se uma descrição feita dos idempotentes centrais primitivos da álgebra de grupo racional de grupos nilpotentes finitos.
Title in English
Primitive central idempotents in some group algebras
Keywords in English
Abelian code
Group algebras
Group rings
Idempotents
Minimal code
Abstract in English
Our goal in this project is to present some results about group rings and its applications, as presented in books and articles about this subject. First of all we are going to establish some basic fact about group rings, which can be found mainly in [5], and then we will present the main results, which are more recent, and have been studied in two different articles. In [4], the authors presented a way of evaluating the number of simple components of some finite group algebras, as well presented a way of evaluating idempotent generators of some minimal abelian codes, their dimension and their weights. In [2] there is a complete description of all the primitive central idempotents of the rational group algebra of finite nilpotent groups.
 
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Publishing Date
2016-03-08
 
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