Noun Phrase
/ˈæb.sə.luːt.li ˌɪr.ɪˈduː.sə.bəl ɡruːp/
An "absolutely irreducible group" is a term used in the context of algebra, specifically in the study of group theory and representations of groups. In this context, it refers to a group representation that cannot be decomposed into smaller representations.
The mathematician demonstrated that the representation of the group was absolutely irreducible.
(El matemático demostró que la representación del grupo era absolutamente irreducible.)
Identifying an absolutely irreducible group often involves advanced techniques in linear algebra.
(Identificar un grupo absolutamente irreducible a menudo implica técnicas avanzadas en álgebra lineal.)
New insights into absolutely irreducible groups can lead to breakthroughs in understanding symmetries.
(Nuevas perspectivas sobre grupos absolutamente irreducibles pueden llevar a avances en la comprensión de simetrías.)
While "absolutely irreducible group" itself is a specialized mathematical phrase and not commonly found in idiomatic expressions, there are related concepts in mathematics that can be expressed idiomatically:
"The whole is greater than the sum of its parts."
Often used to describe systems, including groups, where individual components contribute to an overall structure that cannot be simplified.
(A menudo se utiliza para describir sistemas, incluidos grupos, donde los componentes individuales contribuyen a una estructura general que no se puede simplificar.)
"To break it down."
Used in a mathematical context to describe the process of decomposing elements into simpler components, often the opposite of dealing with an absolutely irreducible group.
(Utilizado en un contexto matemático para describir el proceso de descomponer elementos en componentes más simples, a menudo lo opuesto a tratar con un grupo absolutamente irreducible.)
"No simple solution."
This phrase suggests complexity, akin to an absolutely irreducible representation where a straightforward approach cannot be applied.
(Esta frase sugiere complejidad, similar a una representación absolutamente irreducible donde no se puede aplicar un enfoque directo.)
The term "absolutely irreducible group" derives from several roots in English: - "Absolutely" comes from Latin "absolutus," meaning 'free from restraint'. - "Irreducible" traces back to Latin "irreducibilis," indicating something that cannot be reduced or simplified. - "Group" comes from the French "groupe," which has its origins in Latin "groupe," meaning 'a pile' or 'to group together'.