finitely presented groups
[/ˈfaɪnətli prɪˈzɛntɪd ɡrupz/]
nounpl: finitely presented groups
grupos finitamente apresentados
1. In group theory and algebra, groups that can be defined by a finite number of generators and a finite number of relations among those generators
The fundamental group of a closed surface is an example of a finitely presented group.
O grupo fundamental de uma superfície fechada é um exemplo de um grupo finitamente apresentado.
2. Groups expressible in the form ⟨g₁, g₂, ..., gₙ | r₁, r₂, ..., rₘ⟩ where gᵢ are generators and rⱼ are relational equations
Free groups and groups arising from topology are often finitely presented groups.
Grupos livres e grupos que surgem da topologia são frequentemente grupos finitamente apresentados.
This is specialized mathematical terminology used predominantly in academic and research contexts. The term is identical in both Brazilian Portuguese and European Portuguese academic settings, reflecting the universal nature of mathematical nomenclature. It appears regularly in university-level abstract algebra, topology, and group theory courses throughout Portuguese-speaking countries and internationally.
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