computable groups
[/kəmˈpjuːtəbl ɡruːps/]
nounpl: computable groups
grupos computáveis
1. In mathematics and computability theory, groups whose group operations and properties can be computed by an algorithm or Turing machine; groups with a recursive structure that allows for algorithmic decision procedures.
Computable groups are fundamental objects of study in computability theory and abstract algebra.
Grupos computáveis são objetos fundamentais de estudo na teoria da computabilidade e álgebra abstrata.
2. Groups where the group operation, identity element, and inverse elements can be effectively determined through computational means.
Not all finitely presented groups are computable groups, as some have undecidable word problems.
Nem todos os grupos finitamente apresentados são grupos computáveis, já que alguns têm problemas de palavras indecidíveis.
This is specialized mathematical terminology used primarily in academic and research contexts in both Brazil and English-speaking countries. It is not commonly used in everyday conversation and is specific to the fields of mathematics, computer science, and logic. The term reflects the intersection of classical group theory with modern computability theory, which gained prominence in the 20th century.
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