1. In mathematics, a group equipped with a total order that is compatible with the group operation, meaning if a ≤ b then ca ≤ cb and ac ≤ bc for all elements a, b, c in the group.
The integers under addition form an ordered group with the standard ordering.
Os números inteiros sob adição formam um grupo ordenado com a ordenação padrão.
2. A mathematical structure combining algebraic properties of groups with the ordering properties of posets.
An ordered group must satisfy both group axioms and order compatibility conditions.
Um grupo ordenado deve satisfazer tanto os axiomas de grupo quanto as condições de compatibilidade de ordem.
This is specialized mathematical terminology used primarily in abstract algebra and mathematical logic courses. It is domain-specific and maintains the same meaning across English and Portuguese-speaking mathematics communities. The term is used in university-level pure mathematics and is not part of colloquial speech.