permutation groups

[/ˌpɜːmjuˈteɪʃən ɡruːps/]
nounpl: permutation groups
grupos de permutação
1. In abstract algebra and group theory, a mathematical structure consisting of a set of permutations (rearrangements) of elements that form a group under the operation of composition
Permutation groups are fundamental to understanding symmetry in mathematics and physics.
Os grupos de permutação são fundamentais para compreender a simetria na matemática e na física.
2. A subset of the symmetric group S_n consisting of permutations that satisfy specific algebraic properties
The alternating group is a permutation group containing only even permutations.
O grupo alternado é um grupo de permutação contendo apenas permutações pares.
3. Any group that can be represented as a group of bijections acting on a finite or infinite set
Every finite group is isomorphic to a permutation group according to Cayley's theorem.
Todo grupo finito é isomorfo a um grupo de permutação de acordo com o teorema de Cayley.
This is specialized mathematical terminology used primarily in academic and research contexts in both English-speaking countries and Brazil. The term is consistent across different Portuguese-speaking regions and is fundamental to the study of group theory, a core subject in pure mathematics programs at universities worldwide.
Synonyms / Sinônimos
symmetric groupstransformation groupssubstitution groups

Regional Variations

General Brazilian
grupos de permutação
Standard mathematical terminology used in Brazilian universities and textbooks
Portugal
grupos de permutação
Same usage as in Brazil; standard mathematical terminology
Academic English (USA)
permutation groups
Primary term used in mathematical research and education

Related Words

symmetric groupalternating groupcycle notationgroup theoryabstract algebraCayley's theoremgroup action
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