modular group
[ˈmɑːdjələr ɡruːp]
nounpl: modular groups
grupo modular
1. In mathematics, specifically in number theory and geometry, the group of linear fractional transformations of the form z ↦ (az + b)/(cz + d) where a, b, c, d are integers and ad - bc = 1
The modular group acts on the upper half of the complex plane and is fundamental to the theory of modular forms.
O grupo modular atua na metade superior do plano complexo e é fundamental para a teoria das formas modulares.
2. A mathematical structure denoted PSL(2, ℤ) or SL(2, ℤ), which consists of 2×2 matrices with integer entries and determinant 1
The modular group is one of the most important discrete subgroups of the projective special linear group.
O grupo modular é um dos subgrupos discretos mais importantes do grupo linear especial projetivo.
The modular group is a specialized term used primarily in academic mathematics, particularly in number theory and complex analysis. It is not commonly referenced in everyday language in either Brazil or the United States, but is essential vocabulary in mathematical discourse at universities and research institutions.
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