Computação em grupos de permutação finitos com GAP
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2018-03-05
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Universidade Federal de Goiás
Resumo
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.
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Citação
ROMERO, A. T. S. Computação em grupos de permutação finitos com GAP. 2018. 101 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2018.