Computação em grupos de permutação finitos com GAP

• Autor(a) principal: Romero, Angie Tatiana Suárez
• Data de Publicação: 2018
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• dARK ID: ark:/38995/001300000cksb
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/8220
• topic: Teoría de grupos; Grupos de permutação finitos; Álgebra computacional; Theory of groups; Finite permutation groups; Computational algebra; MATEMATICA::ALGEBRA

Cayley’s theorem allows us to represent a finite group as a permutations group of a finite set of points. In general, an action of a finite group G in a finite set, is described as an application of the group G in the symmetric group Sym(Ω). In this work we will describe some algorithms for permutation groups and implement them in the GAP system. We begin by describing a way of representing groups in computers, we calculate orbits, stabilizers in the basic form and by means of Schreier’s vectors. Later we make algorithms to work with primitive and transitive groups, thus arriving at the concept of BSGS, base and strong generator set, for permutation groups with the algorithm SCHREIERSIMS. In the end we work with group homomorphisms, we find the elements of a group through backtrack searches.