groups with infinite generators
[ɡruːps wɪð ˈɪnfɪnɪt ˈdʒɛnəreɪtərz]
noun phrase
grupos com geradores infinitos
1. In abstract algebra, a mathematical group that requires an infinite set of elements (generators) to generate all elements of the group through group operations
The additive group of integers is an example of a group with infinite generators since it cannot be generated by a finite set of elements
O grupo aditivo dos inteiros é um exemplo de grupo com geradores infinitos, pois não pode ser gerado por um conjunto finito de elementos
2. Groups where no finite subset of elements can generate the entire group through repeated applications of the group operation
Free groups with infinitely many generators are fundamental objects in combinatorial group theory
Grupos livres com infinitos geradores são objetos fundamentais na teoria de grupos combinatória
This is specialized mathematical terminology used primarily in academic and research contexts within mathematics departments and theoretical physics. It holds no cultural significance outside academic circles and is used identically across English-speaking countries and Brazil/Portugal.
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