Made available in DSpace on 2014-06-11T19:26:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2006-03-15Bitstream added on 2014-06-13T19:47:19Z : No. of bitstreams: 1 castro_fr_me_sjrp.pdf: 783980 bytes, checksum: fd80e9aa8c69641da08ee43dfa94509d (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O objetivo principal deste trabalho é estudar a Teoria de Cohomologia de Grupos visando apresentar de forma detalhada algumas aplicações dessa teoria na Topologia e na Algebra, mais especificamente na Teoria de Grupos, com destaque para o Teorema de Schur-Zassenhaus e o Teorema de Classificação de p-grupos que possuem um subgrupo ciclico de índice p (p primo). / The aim of this work is to study the Cohomology Theory of Groups in order to present in detailed form some applications of this theory in Topology and in Algebra, more specifically, in the Theory of Groups, with prominence for the Schur-Zassenhaus Theorem and the Theorem of Classification of p-groups which contain a cyclic subgroup of index p, where p is a prime.

Orientador: Ermínia de Lourdes Campello Fanti / Banca: Luiz Queiroz Pergher / Banca: Maria Gorete Carreira Andrade / Resumo: O objetivo principal deste trabalho é estudar a Teoria de Cohomologia de Grupos visando apresentar de forma detalhada algumas aplicações dessa teoria na Topologia e na Algebra, mais especificamente na Teoria de Grupos, com destaque para o Teorema de Schur-Zassenhaus e o Teorema de Classificação de p-grupos que possuem um subgrupo ciclico de índice p (p primo). / Abstract: The aim of this work is to study the Cohomology Theory of Groups in order to present in detailed form some applications of this theory in Topology and in Algebra, more specifically, in the Theory of Groups, with prominence for the Schur-Zassenhaus Theorem and the Theorem of Classification of p-groups which contain a cyclic subgroup of index p, where p is a prime. / Mestre

We study two topics on surface diffeomorphisms, their mapping classes and dynamics. For the mapping classes of a punctured disc, we study the $\ZxZ$ subgroups of the fundamental groups of the corresponding mapping tori. An application is the proof of the fact that a satellite knot with braid pattern is prime. For the mapping classes of the disc minus a Cantor set, we study a special type of reducible mapping class. This has direct application on the embeddings of solenoids in $\mathbb{S}^3$. We also give some examples of other types of mapping classes of the disc minus a Cantor set. For the dynamics of surface diffeomorphisms, we prove three formulas for computing the topological pressure of a $C^1$-generic conservative diffeomorphism with no dominated splitting and show the continuity of topological pressure with respect to these diffeomorphisms. We prove for these generic diffeomorphisms that there is no equilibrium states with positive measure theoretic entropy. In particular, for hyperbolic potentials, there are no equilibrium states. For $C^1$ generic conservative diffeomorphisms on compact surfaces with no dominated splitting and $\phi_m(x):=-\frac{1}{m}\log \Vert D_x f^m\Vert, m \in \mathbb{N}$, we show that there exist equilibrium states with zero entropy and there exists a transition point $t_0$ for the one parameter family $\lbrace t \phi_m\rbrace_{t\geq 0}$, such that there is no equilibrium states for $ t \in [0, t_0)$ and there is an equilibrium state for $t \in [t_0,+\infty)$.