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Item Sobre uma Construção Relacionada ao Quadrado Tensional não-Abeliano de um Grupo(Universidade Federal de Goiás, 2011-07-01) ANDRADE, Agenor Freitas de; RODRIGUES, Paulo Henrique de Azevedo; lattes.cnpq.br/8910130626123426; OLIVEIRA, Ricardo Nunes de; http://lattes.cnpq.br/0563210461148997Let G and Gj be isomorphic groups. We study the group V (G) which is an extension of the non-abelian tensor square of a group G, G G. Looking for V (G) as an operator in the class of groups, we observe that this operator preserves some properties of the group G such as finiteness, nilpotency and solubility. For a p-group finite G we find an upper bound for the order of G G. Finally, we verified computationally, for some groups, and that the results and also the bounds for the orders of the groups shown here are actually respected.Item Condição de Nilpotência para Grupos Localmente Finitos de expoente p e Álgebras de Lie (p-1)- Engel de Característica p (ou 0)(Universidade Federal de Goiás, 2011-04-25) CARVALHO, Lucimeire Alves de; SILVA, Jhone Caldeira; http://lattes.cnpq.br/6848751340618892; LIMA, Aline de Souza; http://lattes.cnpq.br/1518865173435209Let P be a locally finite group of prime exponent p, admitting a finite soluble automorphism group G of order n coprime to p. In this work we study the influence of the centralizers of the automorphisms in G on the structure of P. In this sense we show that if CP(G), the subgroup of fixed points is soluble of derived length d, then P is nilpotent of class bounded in terms of p, n and d. It will be also shown that if a (p-1)-Engel Lie algebra L of characteristic p (or 0) admits a finite soluble automorphism group G of order n coprime to the characteristic of L, such that CL(G), the subalgebra of fixed points, is soluble of derived length d, then the Lie algebra L is nilpotent of class bounded in terms of p, n and d.Item Comutatividade fraca por bijeção entre grupos abelianos(Universidade Federal de Goiás, 2010-06-28) MACEDO, Silvio Sandro Alves de; RODRIGUES, Paulo Henrique de Azevedo; lattes.cnpq.br/8910130626123426; OLIVEIRA, Ricardo Nunes de; http://lattes.cnpq.br/0563210461148997The group of weak commutativity for bijection G(H;K;σ) = {H;K|[h;hσ] = 1, for all h H} belongs is defined as the quotient of the free product H * K the normal closure of {[h;hσ] : h belongs to all H} in H * K. In this dissertation, we studied the results obtained in 2009 by Sidka and Oliveira [7] that support the following conjecture: If H,K ~= Zp X...X Zp, then G(H,K,σ)is a p-group.Item Códigos geometricamente uniformes em espaços hiperbólicos(Universidade Federal de Goiás, 2008-02-15) MACHADO, Ana Paula Faria; SOUZA, Mário José de; http://lattes.cnpq.br/4862963990848505In this dissertation we define geometrically uniform codes in Euclidean spaces, presenting some symmetrical properties of these codes. Build geometrically uniforme partitions and starting these we define generalized coset codes. We generalize the concept of geometrically uniform codes to hyperbolic spaces. We show a characterization of generalized coset codes through the concept of G-linear codes.Item Sobre Anéis de Lie Admitindo Automorfismos de Ordens Finitas e Álgebras de Lie Quase Nilpotentes.(Universidade Federal de Goiás, 2011-02-28) MELO, Emerson Ferreira de; SILVA, Jhone Caldeira; http://lattes.cnpq.br/6848751340618892In this work we present a study on Lie rings and algebras admitting an automorphism of finite order. We emphasize questions on nilpotency. We prove important results of this theory, for example the Higman, Kreknin and Kostrikin s Theorem. Furthermore, let L be a finite dimensional Lie algebra over an algebraically closed field of characteristic 0. Suppose that L admits a nilpotent Lie algebra D with n weights in L, and let m be the dimension of the Fitting null component with respect to D. Then L is almost nilpotent, namely, L contains a nilpotent subalgebra N of {m,n}-bounded codimension and of nbounded nilpotency class. If m = 0, then L is nilpotent of bounded class by a function of n. This theorem was published by E. I. Khukhro and P. Shumyatsky in the paper entitled Lie Algebras with Almost Constant-Free Derivations .Item Séries de Hilbert de algumas álgebras associadas a grafos orientados via cohomologia de conjuntos parcialmente ordenados(Universidade Federal de Goiás, 2011-08-31) REIS, Bruno Trindade; SERCONEK, Shirlei; http://lattes.cnpq.br/2718527331501182We begin with a definition of the algebras Qn, who originated the study of algebra associated to directed graphs. Then, we define key concepts such as Hilbert series, graded and filtered algebras. Among the quadratic algebras, we introduce the Koszul algebras. The Hilbert series is a useful tool to study the Koszulity of a quadratic algebra. The homological interpretation of the coefficients of the Hilbert series of algebras associated with direct graphs allowed us to give conditions Koszulity these algebras in terms of the homological properties of the graph. We use this interpretation to construct algebras with Hilbert series prescribed.Item Limitantes para Códigos de Peso Constante(Universidade Federal de Goiás, 2011-01-28) RODRIGUES, Silvana da Silva; SERCONEK, Shirlei; http://lattes.cnpq.br/2718527331501182; SOUZA, Mário José de; http://lattes.cnpq.br/4862963990848505The main purpose of this dissertation was to construct lower and upper bounds for the cardinality of the error correcting codes for constant-weight, contained in the vector space Fn 3 , where F3 is a field with three elements, knowing parameters such as length and minimum distance code. We present the main results of linear algebra necessary to develop the theory of codes and then the fundamental concepts of more practical class of codes, the linear error correcting codes. We state the Totobola problem and the Football problem, relating them to the theory of codes and present some bounds for the "covering radius problem"for r = 1 , some values of n. In the last chapter, we conclude the work with some examples that illustrate bounds of coverings for Fn 3 , with r = 2 and 3, and the generalization of the problem, where we present the binary covering radius problem, the case of multiple coverages and the extension of the idea, citing bounds for the cardinality of the codes contained in the vector space over a finite field with any arbitrary number of elements.Item Um algoritmo para estimar a dimensão do segundo grupo de homologia de um grupo finitamente apresentado(Universidade Federal de Goiás, 2012-04-12) VIEIRA, Flavio Pinto; SERCONEK, Shirlei; http://lattes.cnpq.br/2718527331501182; ADORNO, Ticianne Proença Bueno; http://lattes.cnpq.br/7769491630579878The main goal of this work is to establish a primary bound for the dimension of the second homology group of a group G, with coefficients in a field k of characteristic p, H2(G;k), using the operating system GAP. It will be presented with several examples, where in some cases, will be calculated the exact dimensions and in other cases only an upper bound.