classe lateral
1. In abstract algebra and group theory, a subset of a group formed by multiplying a fixed element by all elements of a subgroup, resulting in either a left coset or right coset depending on the direction of multiplication
The left coset of subgroup H by element g is the set {gh : h ∈ H}.
A classe lateral esquerda do subgrupo H pelo elemento g é o conjunto {gh : h ∈ H}.
2. A mathematical structure used in group theory to partition a group into disjoint subsets of equal size
The cosets of a normal subgroup form a quotient group.
As classes laterais de um subgrupo normal formam um grupo quociente.
Coset is a highly specialized term used exclusively in academic mathematics, particularly in abstract algebra courses at the university level. It is not part of everyday vocabulary in either English or Portuguese-speaking regions. The term is equally formal and technical in both languages, with 'classe lateral' being the direct Portuguese equivalent used in Brazilian and European mathematics textbooks and instruction.
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