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Conjecturas em anéis de grupo
(Universidade Federal do Espírito Santo, 2018-03-07) Costa, Vagner Pereira; Fehlberg Junior, Renato; Serdà, Javier Sánchez; Silva, Thiago Filipe da
Group rings have a very rich algebraic structure, since to explore it we must resort to techniques other than group theory and ring theory; we must also resort to the theory of algebraic numbers, the representation of groups and algebras and other algebraic theories. Among the subjects of interest in group rings, we highlight some conjectures that will be the objects of study of the present dissertation: the isomorphism problem, the normalizer problem and the Zassenhaus conjectures. On the isomorphism problem and the normalizer problem, we will prove its validity in some particular cases and it will be presented the known counterexamples. On the Zassenhaus conjectures, we will enunciate and present for which group classes they were proved. We will show how these conjectures relate to the isomorphism problem.