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Master's Dissertation
DOI
Document
Author
Full name
Dylene Agda Souza de Barros
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2010
Supervisor
Committee
Grichkov, Alexandre (President)
Guzzo Junior, Henrique
Zubkov, Alexandr
Title in Portuguese
Estrutura e exemplos de A-Loops comutativos finitos
Keywords in Portuguese
A-loops
A-loops comutativos de expoente 2
A-loops comutativos de ordem mpar
A-loops comutativos de ordem p 3
Aplicações internas
Decomposição
Extensões centrais
Abstract in Portuguese
Esse trabalho trata um pouco da teoria de A-loops comutativos finitos. No primeiro captulo estudamos propriedades básicas de loops em geral e exi- bimos exemplos de loops não associativos. No captulo 2 falamos de A-loops em geral e mesmo sem assumirmos comutatividade obtivemos resultados importantes, um exemplo é que A-loop associa potências. Também determinamos quando um isótopo e K -holomorfo de um A-loop é um A-loop. No captulo 3, nossos únicos objetos de estudo foram os A-loops comutativos finitos. Vimos que tais estruturas têm proriedades muito interessantes, por exemplo, para um A-loop comutativo finito valem os teoremas de Lagrange, Cauchy. Também, um A-loop comutativo finito, Q, tem ordem potência de um primo p se e somente se todo elemento de Q tem ordem potência de p. Mais ainda, todo A-loop comutativo finito de ordem mpar é solúvel. No último captulo, apresentamos algumas maneira de se construir um A-loop.
Title in English
A-Loops structure and examples finite commutative
Keywords in English
A-loops
Central extension
Commutative A-loop of order p 3
Commutative A-loops of exponent 2
Commutative A-loops of odd order
Decomposition
Inner mappings
Abstract in English
In the first chapter we studied basic properties of general loops and we showed some examples of nonassociative loops. In chapter 2, we talked about general A-loops (without commutativity) and even that we obtained important results, for instance, that any A-loop is power-associative. We also determined when an isotope and a K -holomorph of an A-loop is an A-loop. In chapter 3 we dealt only with finite commutative A-loops. We saw that such structures have very interesting properties, for example, for a finite commutative A- loop, Lagrange, Cauchys theorems apply. Also a finite commutative A-loop, Q, has order a power of a prime p if and only if every element of Q has order a power of p. Moreover, finite commutative A-loops of odd order are solvable. In the last chapter we introduce some ways to construct a commutative A-loop
 
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Publishing Date
2019-09-26
 
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