Dans la première partie, on étudie la probabilité de retour des groupes métabéliens de type fini. On donne une caractérisation des tels groupes avec grande probabilité de retour en des termes purement algébriques, à l’aide de la dimension de Krull. Cela nécessite, pour les groupes métabéliens, une variation d’un théorème de Kaloujnine et Krasner qui respecte cette dimension. Au passage, on obtient des bornes inférieures et supérieures sur la probabilité de retour des groupes métabéliens en fonction de la dimension de Krull. La seconde partie concerne les profils isopérimétriques des groupes localement compacts compactement engendrés, qu’on utilise pour caractériser l’existence d’une suite de paires de Følner. On démontre que le profil isopérimétrique augmente lorsqu’on passe au quotient, avec des constantes indépendantes de l’échelle, améliorant une théorème de Tessera. Combinant les deux, on obtient que l’existence de suites de paires de Følner passe au quotient. On montre qu’elle passe au sous-groupe fermé, généralisant un résultat correspondant d’Erschler pour les groupes de type fini. Cela permet d’obtenir une preuve plus auto-contenue du théorème principal de la première partie.La troisième partie est un travail en commun avec Kropholler dans lequel on étudie la structure des groupes résolubles de rang sans torsion infini n’ayant pas de section isomorphe à ZwrZ. On en déduit qu’en présence d’une dimension de Krull, ce type de section est la seule obstruction à la finitude du rang sans torsion. / In the fist part, we study the return probability of finitely generated metabelian groups. We give a characterization of such groups with large return probability in purely algebraic terms, namely the Krull dimension of the group. To do so, we establish, for metabelian groups, a variation of a famous embedding theorem of Kaloujinine and Krasner that respects this dimension. Along the way, we obtain lower and upper bounds on the return probability of metabelian groups according to their dimension.The second part of this thesis deals with isoperimetric profiles of locally compact compactly generated groups, that we use to characterize the existence of sequences of Følner couples. We generalize at a compact scale previous results of Tessera, in particular that they increase when going to a quotient group, so as to state in more generality a result from the first part, namely that the existence of Følner couples goes to a quotient group. We also prove that it goes to a closed subgroup. This allows to obtains a more self-contained proof of the main result of the first part of this thesis.The third part is a joint work with Kropholler in which we study the structure of soluble groups of infinite torsion-free rank with no ZwrZ. As a corollary, we obtain that a finitely generated soluble group with Krull dimension has finite torsion-free rank if and only if it has no ZwrZ.

Submitted by Liliane Ferreira (ljuvencia30@gmail.com) on 2018-06-26T15:22:18Z No. of bitstreams: 2 Dissertação - Simone Hilário da Silva Brasileiro - 2018.pdf: 2495771 bytes, checksum: 5602d94f04f2286b718be3983d21eafe (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2018-06-27T10:30:16Z (GMT) No. of bitstreams: 2 Dissertação - Simone Hilário da Silva Brasileiro - 2018.pdf: 2495771 bytes, checksum: 5602d94f04f2286b718be3983d21eafe (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2018-06-27T10:30:16Z (GMT). No. of bitstreams: 2 Dissertação - Simone Hilário da Silva Brasileiro - 2018.pdf: 2495771 bytes, checksum: 5602d94f04f2286b718be3983d21eafe (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2018-05-17 / Behavior Analysis is one of the scientific fields that has dealt in a diversified way with the concepts related to the behavior of the individual, and that has produced studies that can allow the understanding of the choices in investment scenarios. Two articles were produced to investigate the effect of the independent variables, market attributes and rate of return on the invested value. The objective of study 1 is to analyze the effect of market attributes on the choice of Investments. While study 2 seeks to respond to the limitations presented in article 1, it aims to verify the effect of rates of return on the choice of investments together with the number of attributes of the markets, verifying the influence of these variables on the behavior of choice. The research was carried out with 48 university students who were divided in 2 groups with 24 participants each, combined with the independent variables. For the accomplishment of the experiment was programmed a Software, characterized as Invest 1.0, specific for the study. Through the software it was possible to simulate two Markets for investments, A and B, presenting in them four sectors: Bank, Electric, Mining and Oil. The results obtained in study 1 show that the preference of the participants was greater for the market that presented more attributes, even when the market did not present a return. With the exception of the Bank sector, in Group 2, where the participants followed the rate of return and not the attributes, contradicting the function of the number of attributes as reinforcers. While in study 2, it was found that in general the number of attributes together with the return determined the preference of the participants, but some participants presented inconsistent results, pointing out loopholes for later studies that seek to solve them. / A Análise do Comportamento é um dos campos científicos que tem tratado de forma diversificada os conceitos relacionados ao comportamento do indivíduo, e que tem produzido estudos que podem permitir a compreensão das escolhas em cenários de investimentos. Para a realização da pesquisa foram produzidos dois artigos que têm como objetivo investigar o efeito das variáveis independentes, atributos dos mercados e taxa de retorno sobre o valor investido. O objetivo do estudo 1 é analisar o efeito dos atributos dos mercados na escolha de Investimentos. Enquanto que o estudo 2 busca responder as limitações apresentadas no artigo 1, e tem como objetivo verificar o efeito das taxas de retorno sobre a escolha dos investimentos juntamente com o número de atributos dos mercados, verificando a influência destas variáveis no comportamento de escolha. A pesquisa foi realizada com 48 estudantes universitários que foram divididos em 2 grupos com 24 participantes cada, combinados com as variáveis independentes. Para a realização do experimento foi programado um Software, caracterizado como Invest 1.0, específico para o estudo. Através do software foi possível simular dois Mercados para investimentos, A e B, apresentando neles quatro setores: Banco, Elétrica, Mineradora e Petrolífera. Os resultados obtidos nos estudo 1 mostram que a preferência de escolha dos participantes foi maior pelo Mercado que apresentava maior número de atributos, mesmo quando o Mercado não apresentava retorno. Com exceção do setor Banco, no Grupo 2, em que os participantes acompanharam a taxa de retorno e não os atributos, contrariando a função do número de atributos como reforçadores. Enquanto que no estudo 2, verificou-se que em geral o número de atributos juntamente com o retorno determinaram a preferência de escolha dos participantes, mas alguns participantes apresentaram resultados inconsistentes, apontando brechas para estudos posteriores que busquem resolvê-los.