linearly transitive group (english) - meaning, definition, translation, pronunciation

Part of Speech

Noun Phrase

Phonetic Transcription

/lɪˈnɪəriˌli ˈtræn.zɪ.tɪv ɡruːp/

Meaning and Usage

A linearly transitive group is a concept in the field of group theory, particularly in the area of algebra. In this context, it refers to a group acting on a set in such a way that it can move any point to any other point while maintaining a certain order structure (linearity). This concept is primarily used in mathematical and theoretical contexts.

• Frequency of Use: The term is relatively specialized and is primarily used in written mathematical discourse rather than spoken language. Its usage may frequently appear in academic papers, textbooks, and lectures focused on algebra or group theory.

Example Sentences

• The concept of a linearly transitive group can be crucial in understanding symmetry in algebra.

• Понятие линейно транзитивной группы может быть решающим в понимании симметрии в алгебре.

• Researchers are exploring the properties of a linearly transitive group to derive new mathematical theorems.

• Исследователи изучают свойства линейно транзитивной группы, чтобы вывести новые математические теоремы.

• A linearly transitive group provides a framework for analyzing geometric transformations in higher dimensions.

• Линейно транзитивная группа предоставляет основу для анализа геометрических преобразований в более высоких измерениях.

Idiomatic Expressions

The term "linearly transitive group" does not have commonly recognized idiomatic expressions associated with it because it is a specialized mathematical term. However, here are a couple of related expressions in mathematics:

• Group action: The way in which a group can act upon a set, creating different configurations.

• Групповое действие позволяет анализировать, как группа взаимодействует с множеством.

• Transitive relation: A binary relation R is transitive if whenever aRb and bRc, then aRc.

• Транзитивное отношение возникает, когда aRb и bRc, тогда aRc.

Etymology

The term "linearly transitive group" derives from the combination of several roots: - Linearly comes from the term "linear," which originates from the Latin "linearis" meaning "pertaining to a line." - Transitive is from the Latin "transitivus," which means "having the quality of passing over." - Group is derived from the Latin "gruppus," from the Italian "gruppo," meaning a collection or bundle.

Synonyms and Antonyms

• Synonyms: N/A in a strict sense due to its specialized nature, but terms like "transitive group" or "permutation group" might be related in certain contexts.
• Antonyms: "Non-transitive group" (though it's not commonly used).

This term is a precise description within algebra and does not vary much in usage across different contexts.