free groups
[/friː ɡruːps/]
nounpl: free groups
grupos livres
1. In mathematics and group theory, groups generated by a set of elements with no relations among them other than those required by the group axioms
Free groups are fundamental objects in algebra and topology.
Grupos livres são objetos fundamentais em álgebra e topologia.
2. Groups with generators and no defining relations, allowing maximum freedom in their structure
The free group on two generators has a well-studied structure.
O grupo livre gerado por dois elementos possui uma estrutura bem estudada.
3. Mathematical structures used in combinatorial group theory and symbolic logic
Free groups appear naturally in the study of fundamental groups of graphs.
Grupos livres aparecem naturalmente no estudo de grupos fundamentais de grafos.
This is specialized mathematical terminology used primarily in academic and research contexts. The term is consistent across Portuguese-speaking countries in mathematics education and research, with no regional variations.
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